Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi-Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.

Effect of substitution on molecular conformation and packing features in a series of aryl substituted ethyl-6-methyl-4-phenyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylates

The supramolecular structures of eight aryl protected ethyl-6-methyl-4-phenyl-2-thioxo-1,2,3,4 tetrahydropyrimidine-5-carboxyl ates were analyzed in order to understand the effect of variations in functional groups on molecular geometry, conformation and packing of molecules in the crystalline lattice. It is observed that the existence of a short intra-molecular C-H center dot center dot center dot pi interaction between the aromatic hydrogen of the aryl ring with the isolated double bond of the six-membered tetrahydropyrimidine ring is a key feature which imparts additional stability to the molecular conformation in the solid state. The compounds pack via the cooperative involvement of both N-H center dot center dot center dot S=C and N-H center dot center dot center dot O=C intermolecular dimers forming a sheet like structure. In addition, weak C-H center dot center dot center dot O and C-H center dot center dot center dot pi intermolecular interactions provide additional stability to the crystal packing.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Shock acceleration in the solar corona

In this thesis acceleration of energetic particles at collisionless shock waves in space plasmas is studied using numerical simulations, with an emphasis on physical conditions applicable to the solar corona. The thesis consists of four research articles and an introductory part that summarises the main findings reached in the articles and discusses them with respect to theory of diffusive shock acceleration and observations. This thesis gives a brief review of observational properties of solar energetic particles and discusses a few open questions that are currently under active research. For example, in a few large gradual solar energetic particle events the heavy ion abundance ratios and average charge states show characteristics at high energies that are typically associated with flare-accelerated particles, i.e. impulsive events. The role of flare-accelerated particles in these and other gradual events has been discussed a lot in the scientific community, and it has been questioned if and how the observed features can be explained in terms of diffusive shock acceleration at shock waves driven by coronal mass ejections. The most extreme solar energetic particle events are the so-called ground level enhancements where particle receive so high energies that they can penetrate all the way through Earth's atmosphere and increase radiation levels at the surface. It is not known what conditions are required for acceleration into GeV/nuc energies, and the presence of both very fast coronal mass ejections and X-class solar flares makes it difficult to determine what is the role of these two accelerators in ground level enhancements. The theory of diffusive shock acceleration is reviewed and its predictions discussed with respect to the observed particle characteristics. We discuss how shock waves can be modeled and describe in detail the numerical model developed by the author. The main part of this thesis consists of the four scientific articles that are based on results of the numerical shock acceleration model developed by the author. The novel feature of this model is that it can handle complex magnetic geometries which are found, for example, near active regions in the solar corona. We show that, according to our simulations, diffusive shock acceleration can explain the observed variations in abundance ratios and average charge states, provided that suitable seed particles and magnetic geometry are available for the acceleration process in the solar corona. We also derive an injection threshold for diffusive shock acceleration that agrees with our simulation results very well, and which is valid under weakly turbulent conditions. Finally, we show that diffusive shock acceleration can produce GeV/nuc energies under suitable coronal conditions, which include the presence of energetic seed particles, a favourable magnetic geometry, and an enhanced level of ambient turbulence.

In situ transmission electron microscope study of single asperity sliding contacts

Direct observation of events taking place at the contacting interfaces is important to understand many tribological phenomena. Transmission electron microscope (TEM) has the ability to look through materials at very high magnifications. Most of the TEM observations are done long after the deforming loads and stresses have been relaxed and the material state is further disturbed during the specimen preparation. We have developed a specimen holder in which two electron transparent surfaces can be brought in contact and moved relative to each other in JEOL 2000FX microscope. This holder enables visualization of not only the contacting surfaces at nanoscale but also the subsurface deformation resulting from the contact interaction. Sliding experimentS have been carried out mimicking a single asperity sliding contact. A sharp tungsten probe is moved laterally against a tip mounted on a cantilever. Magnitude of the contact instability, when the contact is broken is found to be dependent on the local geometry of the contact.(C) 2009 Elsevier Ltd. All rights reserved.

Multiwavelength studies of regolith effects in planetary remote sensing

A large proportion of our knowledge about the surfaces of atmosphereless solar-system bodies is obtained through remote-sensing measurements. The measurements can be carried out either as ground-based telescopic observations or space-based observations from orbiting spacecraft. In both cases, the measurement geometry normally varies during the observations due to the orbital motion of the target body, the spacecraft, etc.. As a result, the data are acquired over a variety of viewing and illumination angles. Surfaces of planetary bodies are usually covered with a layer of loose, broken-up rock material called the regolith whose physical properties affect the directional dependence of remote-sensed measurements. It is of utmost importance for correct interpretation of the remote-sensed data to understand the processes behind this alteration. In the thesis, the multi-angular effects that the physical properties of the regolith have on remote-sensing measurements are studied in two regimes of electromagnetic radiation, visible to near infrared and soft X-rays. These effects are here termed generally the regolith effects in remote sensing. Although the physical mechanisms that are important in these regions are largely different, notable similarities arise in the methodology that is used in the study of the regolith effects, including the characterization of the regolith both in experimental studies and in numerical simulations. Several novel experimental setups have been constructed for the thesis. Alongside the experimental work, theoretical modelling has been carried out, and results from both approaches are presented. Modelling of the directional behaviour of light scattered from a regolith is utilized to obtain shape and spin-state information of several asteroids from telescopic observations and to assess the surface roughness and single-scattering properties of lunar maria from spacecraft observations. One of the main conclusions is that the azimuthal direction is an important factor in detailed studies of planetary surfaces. In addition, even a single parameter, such as porosity, can alter the light scattering properties of a regolith significantly. Surface roughness of the regolith is found to alter the elemental fluorescence line ratios of a surface obtained through planetary soft X-ray spectrometry. The results presented in the thesis are among the first to report this phenomenon. Regolith effects need to be taken into account in the analysis of remote-sensed data, providing opportunities for retrieving physical parameters of the surface through inverse methods.

Knowledge through Discussion : An Interpretation of Epistemology in Plato's Meno

According to Meno s paradox we cannot inquire into what we do not know because we do not know what we are inquiring into. There are many ways to interpret the paradox but the central issue about our ability to reach truth is a profound one. In the dialogue Meno, Plato presents the paradox and an outline of a solution which enables us to reach knowledge (epistēmē) through philosophical discussion. During the last century Meno has often been considered transitional between Socratic thinking and Plato s own philosophy, and thus the dialogue has not been adequately interpreted as an integrated whole. Therefore the distinctive epistemology of the dialogue has not gained due notice. In this thesis the dialogue is analysed as an integrated whole and the philosophical interpretation also takes into account its dramatic features. The thesis emphasises the role of language and definitions in acquiring knowledge. Among the results concerning these subjects is a new interpretation of Socrates s defintion of shape (schēma). The theory of anamnēsis all learning is recollection in the Meno is argued to answer the paradox philosophically although Plato s presentation also contains playful and ironic elements. The background of the way Plato presents his case is that he appreciated the fact that no argument can plausibly demonstrate that argumentation is able to reach truth. In the Meno, Plato makes the earliest explicit distinction between knowledge and true belief in the history of Western philosophy. He also gives a definition of knowledge which is the basis of the so called classical definition of knowledge as justified true belief. In the Meno, true beliefs become knowledge when someone ties them down by reasoning about the explanation. The analysis of the epistemology of the dialogue from this perspective gives an interpretation which integrates the central concepts of the epistemology in the dialogue elenchos, anamnēsis and hypothetical inquiry into a unified whole which contains a plausible argument according to which the ignorant can reach knowledge through discussion. The conception that emerges by such an analysis is interesting both from the point of view of current interests and that of the history of philosophy. The method of knowledge acquisition in the Meno can, for example, be seen as a predecessor of modern scientific methods. The Meno is the earliest Greek mathematical text that has survived in its original form. The analysis presented in the thesis of the geometric passages in the dialogue provides new results both concerning Socrates s geometry lesson with the slave and the example presenting the hypothetical method. Concerning the latter, a new interpretation is presented. Keywords: anamnēsis, epistēmē, knowledge, Meno s paradox, Plato

The 5-Methyl Group in Thymine Dynamically Influences the Structure of A-Tracts in DNA at the Local and Global Level

DNA sequences containing a stretch of several A:T basepairs without a 5'-TA-3' step are known as A-tracts and have been the subject of extensive investigation because of their unique structural features such as a narrow minor groove and their crucial role in several biological processes. One of the aspects under investigation has been the influence of the 5-methyl group of thymine on the properties of A-tracts. Detailed molecular dynamics simulation studies of the sequences d(CGCAAAUUUGCG) and d(CGCAAATTTGCG) indicate that the presence of the 5-methyl group in thymine increases the frequency of a narrow minor groove conformation, which could facilitate its specific recognition by proteins, and reduce its susceptibility to cleavage by DNase I. The bias toward a wider minor groove in the absence of the thymine 5-methyl group is a static structural feature. Our results also indicate that the presence of the thymine 5-methyl group is necessary for calibrating the backbone conformation and the basepair and dinucleotide step geometry of the core A-tract as well as the flanking CA/TG and the neighboring GC/GC steps, as observed in free and protein-bound DNA. As a consequence, it also fine-tunes the curvature of the longer DNA fragment in which the A-tract is embedded.

Interface stresses in a composite cylindrical shell under ring loading

The problem of a two-layer circular cylindrical shell subjected to radial ring loading has been solved theoretically. The solution is developed by uniting the elasticity solution through Love function approach for the inner thick shell with the Flügge shell theory for the thin outer shell. Numerical work has been done with a digital computer for different values of shell geometry parameters and material constants. The general behaviour of the composite shell has been studied in the light of these numerical results.

Two-stream instability in plasma

The problem of two-stream instability in plasma is studied by specifying the importance of initial magnetic field associated with the motion of the charged particles and the boundary effects. In Part I the accurate initial steady state is studied when the streams of electrons and ions move with different uniform speeds in plasmas with plane and cylindrical geometry. In Part II, in order to show the effects of finiteness and inhomogeneity of the system, small transverse plasma oscillations are studied in the case of plane plasmas. The role of plasma-sheath oscillations at the boundaries is found to be very important in driving the instabilities associated with the electromagnetic modes. The numerical estimates of the growth rates of the instability are given for the specific case of the physical data in discharge tubes.

A symmetric solution for a cylindrical shell enclosed in an elastic casing

The problem of a long, thin circular cylindrical shell enclosed in an elastic casing and subjected to a ring of radial load on the inner rim is solved using the Love function for the casing in conjunction with Flügge shell theory. Numerical work has been done with a digital computer and the results for stress and displacement fields are given for various values of the shell geometry parameters and material constants.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

A Comparative Study of Aromaticity in Substituted Tetracyclic and Hexacyclic Thiophenes

We have studied the nature of aromaticity in expanded porphyrinic analogues of thiophenes formed by four and six thiophenes. Using density functional theory (DFT) we have analyzed the aromaticity of both the macrocycle and individual molecular fragments. We find paramagnetic annulenic ring currents in the case of tetracyclic molecules and diamagnetic annulenic ring currents for hexacyclic molecules. We have also studied the effect of substitution of benzene rings within the macrocycle. We find that as the number of benzene rings is increased the aromaticity increases for tetracyclic systems and decreases for hexacyclic systems. All the results have been analyzed with various microscopic parameters, including geometry, excitation gap, and NMR criteria.

Enhanced Ion Anisotropy by Nonconventional Coordination Geometry: Single-Chain Magnet Behavior for a [{(FeL)-L-II}(2){Nb-IV(CN)(8)}] Helical Chain Compound Designed with Heptacoordinate Fe-II

Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {(FeNbIV)-Nb-II} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb-IV, Mo-IV, W-IV.) X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H2O)Fe(L-1)}{M(CN)(8)}{Fe(L-1)}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L-1)}(2+) and {M(CN)(8)}(4-) units (L-1 stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L-1)) unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L-1)(H2O)(2)]Cl-2 a negative zero field splitting parameter of D approximate to -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L-1)(H2O)(2)]Cl-2 are also reported.