10 resultados para Elastic constants
em ArchiMeD - Elektronische Publikationen der Universität Mainz - Alemanha
Resumo:
We investigate a chain consisting of two coupled worm-like chains withconstant distance between the strands. The effects due todouble-strandedness of the chain are studied. In a previous analyticalstudy of this system an intrinsic twist-stretch coupling and atendency of kinking is predicted. Even though a local twist structureis observed the predicted features are not recovered. A new model for DNA at the base-pair level is presented. Thebase-pairs are treated as flat rigid ellipsoids and thesugar-phosphate backbones are represented as stiff harmonic springs.The base-pair stacking interaction is modeled by a variant of theGay-Berne potential. It is shown by systematic coarse-graininghow the elastic constants of a worm-like chain are related to thelocal fluctuations of the base-pair step parameters. Even though a lotof microscopic details of the base-pair geometry is neglected themodel can be optimized to obtain a B-DNA conformation as ground stateand reasonable elastic properties. Moreover the model allows tosimulate much larger length scales than it is possible with atomisticsimulations due to the simplification of the force-field and inparticular due to the possibility of non-local Monte-Carlo moves. Asa first application the behavior under stretching is investigated. Inagreement with micromanipulation experiments on single DNA moleculesone observes a force-plateau in the force-extension curvescorresponding to an overstretching transition from B-DNA to aso-called S-DNA state. The model suggests a structure for S-DNA withhighly inclined base-pairs in order to enable at least partialbase-pair stacking. Finally a simple model for chromatin is introduced to study itsstructural and elastic properties. The underlying geometry of themodeled fiber is based on a crossed-linker model. The chromatosomesare treated as disk-like objects. Excluded volume and short rangenucleosomal interaction are taken into account by a variant of theGay-Berne potential. It is found that the bending rigidity and thestretching modulus of the fiber increase with more compact fibers. Fora reasonable parameterization of the fiber for physiologicalconditions and sufficiently high attraction between the nucleosomes aforce-extension curve is found similar to stretching experiments onsingle chromatin fibers. For very small stretching forces a kinkedfiber forming a loop is observed. If larger forces are applied theloop formation is stretched out and a decondensation of the fibertakes place.
Resumo:
Development of empirical potentials for amorphous silica Amorphous silica (SiO2) is of great importance in geoscience and mineralogy as well as a raw material in glass industry. Its structure is characterized as a disordered continuous network of SiO4 tetrahedra. Many efforts have been undertaken to understand the microscopic properties of silica by classical molecular dynamics (MD) simulations. In this method the interatomic interactions are modeled by an effective potential that does not take explicitely into account the electronic degrees of freedom. In this work, we propose a new methodology to parameterize such a potential for silica using ab initio simulations, namely Car-Parrinello (CP) method [Phys. Rev. Lett. 55, 2471 (1985)]. The new potential proposed is compared to the BKS potential [Phys. Rev. Lett. 64, 1955 (1990)] that is considered as the benchmark potential for silica. First, CP simulations have been performed on a liquid silica sample at 3600 K. The structural features so obtained have been compared to the ones predicted by the classical BKS potential. Regarding the bond lengths the BKS tends to underestimate the Si-O bond whereas the Si-Si bond is overestimated. The inter-tetrahedral angular distribution functions are also not well described by the BKS potential. The corresponding mean value of theSiOSi angle is found to be ≃ 147◦, while the CP yields to aSiOSi angle centered around 135◦. Our aim is to fit a classical Born-Mayer/Coulomb pair potential using ab initio calculations. To this end, we use the force-matching method proposed by Ercolessi and Adams [Europhys. Lett. 26, 583 (1994)]. The CP configurations and their corresponding interatomic forces have been considered for a least square fitting procedure. The classical MD simulations with the resulting potential have lead to a structure that is very different from the CP one. Therefore, a different fitting criterion based on the CP partial pair correlation functions was applied. Using this approach the resulting potential shows a better agreement with the CP data than the BKS ones: pair correlation functions, angular distribution functions, structure factors, density of states and pressure/density were improved. At low temperature, the diffusion coefficients appear to be three times higher than those predicted by the BKS model, however showing a similar temperature dependence. Calculations have also been carried out on crystalline samples in order to check the transferability of the potential. The equilibrium geometry as well as the elastic constants of α-quartz at 0 K are well described by our new potential although the crystalline phases have not been considered for the parameterization. We have developed a new potential for silica which represents an improvement over the pair potentials class proposed so far. Furthermore, the fitting methodology that has been developed in this work can be applied to other network forming systems such as germania as well as mixtures of SiO2 with other oxides (e.g. Al2O3, K2O, Na2O).
Resumo:
In this thesis foliation boudinage and related structures have been studied based on field observations and numerical modeling. Foliation boudinage occurs in foliated rocks independent of lithology contrast. The developing structures are called ‘Foliation boudinage structures (FBSs)’ and show evidence for both ductile and brittle deformation. They are recognized in rocks by perturbations in monotonous foliation adjacent to a central discontinuity, mostly filled with vein material. Foliation boudinage structures have been studied in the Çine Massif in SW-Turkey and the Furka Pass-Urseren Zone in central Switzerland. Four common types have been distinguished in the field, named after vein geometries in their boudin necks in sections normal to the boudin axis: lozenge-, crescent-, X- and double crescent- type FBSs. Lozengetype FBSs are symmetric and characterized by lozenge-shaped veins in their boudin neck with two cusps facing opposite sides. A symmetrical pair of flanking folds occurs on the two sides of the vein. Crescent-type FBSs are asymmetric with a single smoothly curved vein in the boudin neck, with vein contacts facing to one side. X- and double crescent- type FBSs are asymmetric. The geometry of the neck veins resembles that of cuspate-lobate structures. The geometry of flanking structures is related to the shape of the veins. The veins are mostly filled with massive quartz in large single crystals, commonly associated with tourmaline, feldspar and biotite and in some cases with chlorite. The dominance of large facetted single quartz crystals and spherulitic chlorite in the veins suggest that the minerals grew into open fluidfilled space. FLAC experiments show that fracture propagation during ductile deformation strongly influences the geometry of developing veins. The cusps of the veins are better developed in the case of propagating fractures. The shape of the boudin neck veins in foliation boudinage depends on the initial orientation and shape of the fracture, the propagation behaviour of the fracture, the geometry of bulk flow, and the stage at which mineral filling takes place. A two dimensional discrete element model was used to study the progressive development of foliation boudinage structures and the behavior of visco-elastic material deformed under pure shear conditions. Discrete elements are defined by particles that are connected by visco-elastic springs. Springs can break. A number of simulations was Abstract vii performed to investigate the effect of material properties (Young’s modulus, viscosity and breaking strength) and anisotropy on the developing structures. The models show the development of boudinage in single layers, multilayers and in anisotropic materials with random mica distribution. During progressive deformation different types of fractures develop from mode I, mode II to the combination of both. Voids develop along extension fractures, at intersections of conjugate shear fractures and in small pull-apart structures along shear fractures. These patterns look similar to the natural examples. Fractures are more localized in the models where the elastic constants are low and the competence contrast is high between the layers. They propagate through layers where the constants are high and the competence contrast is relatively low. Flow localize around these fractures and voids. The patterns similar to symmetric boudinage structures and extensional neck veins (e.g. lozenge type) more commonly develop in the models with lower elastic constants and anisotropy. The patterns similar to asymmetric foliation boudinage structures (e.g. X-type) develop associated with shear fractures in the models where elastic constants and anisotropy of the materials are relatively high. In these models boudin neck veins form commonly at pull-aparts along the shear fractures and at the intersection of fractures.
Resumo:
Phononic crystals, capable to block or direct the propagation of elastic/acoustic waves, have attracted increasing interdisciplinary interest across condensed matter physics and materials science. As of today, no generalized full description of elastic wave propagation in phononic structures is available, mainly due to the large number of variables determining the band diagram. Therefore, this thesis aims for a deeper understanding of the fundamental concepts governing wave propagation in mesoscopic structures by investigation of appropriate model systems. The phononic dispersion relation at hypersonic frequencies is directly investigated by the non-destructive technique of high-resolution spontaneous Brillouin light scattering (BLS) combined with computational methods. Due to the vector nature of the elastic wave propagation, we first studied the hypersonic band structure of hybrid superlattices. These 1D phononic crystals composed of alternating layers of hard and soft materials feature large Bragg gaps. BLS spectra are sensitive probes of the moduli, photo-elastic constants and structural parameters of the constituent components. Engineering of the band structure can be realized by introduction of defects. Here, cavity layers are employed to launch additional modes that modify the dispersion of the undisturbed superlattice, with extraordinary implications to the band gap region. Density of states calculations in conjunction with the associated deformation allow for unambiguous identication of surface and cavity modes, as well as their interaction with adjacent defects. Next, the role of local resonances in phononic systems is explored in 3D structures based on colloidal particles. In turbid media BLS records the particle vibration spectrum comprising resonant modes due to the spatial confinement of elastic energy. Here, the frequency and lineshapes of the particle eigenmodes are discussed as function of increased interaction and departure from spherical symmetry. The latter is realized by uniaxial stretching of polystyrene spheres, that can be aligned in an alternating electric field. The resulting spheroidal crystals clearly exhibit anisotropic phononic properties. Establishing reliable predictions of acoustic wave propagation, necessary to advance, e.g., optomechanics and phononic devices is the ultimate aim of this thesis.
Resumo:
This dissertation is devoted to the experimental exploration of the propagation of elastic waves in soft mesoscopic structures with submicrometer dimensions. A strong motivation of this work is the large technological relevance and the fundamental importance of the subject. Elastic waves are accompanied by time-dependent fluctuations of local stress and strain fields in the medium. As such, the propagation phase velocities are intimately related to the elastic moduli. Knowledge of the elastic wave propagation directly provides information about the mechanical properties of the probed mesoscopic structures, which are not readily accessible experimentally. On the other hand, elastic waves, when propagating in an inhomogeneous medium with spatial inhomogeneities comparable to their wavelength, exhibit rather rich behavior, including the appearance of novel physical phenomena, such as phononic bandgap formation. So far, the experimental work has been restricted to macroscopic structures, which limit wave propagation below the KHz range. It was anticipated that an experimental approach capable of probing the interplay of the wave propagation with the controlled mesoscopic structures would contribute to deeper insights into the fundamental problem of elastic wave propagation in inhomogeneous systems. The mesoscopic nature of the structures to be studied precludes the use of traditional methods, such as sound transmission, for the study of elastic wave propagation. In this work, an optical method utilizing the inelastic scattering of photons by GHz frequency thermally excited elastic waves, known as Brillouin light scattering spectroscopy (BLS), was employed. Two important classes of soft structures were investigated: thin films and colloidal crystals. For the former, the main interest was the effect of the one-dimensional (1D) confinement on the wave propagation due to the presence of the free-surface or interface of the layer and the utilization of these waves to extract relevant material parameters. For the second system, the primary interest was the interaction of the elastic wave and the strong scattering medium with local resonance units in a three-dimensional (3D) periodic arrangement.
Resumo:
The proton-nucleus elastic scattering at intermediate energies is a well-established method for the investigation of the nuclear matter distribution in stable nuclei and was recently applied also for the investigation of radioactive nuclei using the method of inverse kinematics. In the current experiment, the differential cross sections for proton elastic scattering on the isotopes $^{7,9,10,11,12,14}$Be and $^8$B were measured. The experiment was performed using the fragment separator at GSI, Darmstadt to produce the radioactive beams. The main part of the experimental setup was the time projection ionization chamber IKAR which was simultaneously used as hydrogen target and a detector for the recoil protons. Auxiliary detectors for projectile tracking and isotope identification were also installed. As results from the experiment, the absolute differential cross sections d$sigma$/d$t$ as a function of the four momentum transfer $t$ were obtained. In this work the differential cross sections for elastic p-$^{12}$Be, p-$^{14}$Be and p-$^{8}$B scattering at low $t$ ($t leq$~0.05~(GeV/c)$^2$) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The analysis of the differential cross section for the isotope $^{14}$Be shows that a good description of the experimental data is obtained when density distributions consisting of separate core and halo components are used. The determined {it rms} matter radius is $3.11 pm 0.04 pm 0.13$~fm. In the case of the $^{12}$Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of $2.82 pm 0.03 pm 0.12$~fm was determined. An interesting result is that the free $^{12}$Be nucleus behaves differently from the core of $^{14}$Be and is much more extended than it. The data were also compared with theoretical densities calculated within the FMD and the few-body models. In the case of $^{14}$Be, the calculated cross sections describe the experimental data well while, in the case of $^{12}$Be there are discrepancies in the region of high momentum transfer. Preliminary experimental results for the isotope $^8$B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is $2.60pm 0.02pm 0.26$~fm. The data were compared with microscopic calculations in the frame of the FMD model and reasonable agreement was observed. The results obtained in the present analysis are in most cases consistent with the previous experimental studies of the same isotopes with different experimental methods (total interaction and reaction cross section measurements, momentum distribution measurements). For future investigation of the structure of exotic nuclei a universal detector system EXL is being developed. It will be installed at the NESR at the future FAIR facility where higher intensity beams of radioactive ions are expected. The usage of storage ring techniques provides high luminosity and low background experimental conditions. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented.
Resumo:
Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.
Resumo:
As the elastic response of cell membranes to mechanical stimuli plays a key role in various cellular processes, novel biophysical strategies to quantify the elasticity of native membranes under physiological conditions at a nanometer scale are gaining interest. In order to investigate the elastic response of apical membranes, elasticity maps of native membrane sheets, isolated from MDCK II (Madine Darby Canine kidney strain II) epithelial cells, were recorded by local indentation with an Atomic Force Microscope (AFM). To exclude the underlying substrate effect on membrane indentation, a highly ordered gold coated porous array with a pore diameter of 1.2 μm was used to support apical membranes. Overlays of fluorescence and AFM images show that intact apical membrane sheets are attached to poly-D-lysine coated porous substrate. Force indentation measurements reveal an extremely soft elastic membrane response if it is indented at the center of the pore in comparison to a hard repulsion on the adjacent rim used to define the exact contact point. A linear dependency of force versus indentation (-dF/dh) up to 100 nm penetration depth enabled us to define an apparent membrane spring constant (kapp) as the slope of a linear fit with a stiffness value of for native apical membrane in PBS. A correlation between fluorescence intensity and kapp is also reported. Time dependent hysteresis observed with native membranes is explained by a viscoelastic solid model of a spring connected to a Kelvin-Voight solid with a time constant of 0.04 s. No hysteresis was reported with chemically fixated membranes. A combined linear and non linear elastic response is suggested to relate the experimental data of force indentation curves to the elastic modulus and the membrane thickness. Membrane bending is the dominant contributor to linear elastic indentation at low loads, whereas stretching is the dominant contributor for non linear elastic response at higher loads. The membrane elastic response was controlled either by stiffening with chemical fixatives or by softening with F-actin disrupters. Overall, the presented setup is ideally suitable to study the interactions of the apical membrane with the underlying cytoskeleton by means of force indentation elasticity maps combined with fluorescence imaging.
Resumo:
The electromagnetic form factors of the proton are fundamental quantities sensitive to the distribution of charge and magnetization inside the proton. Precise knowledge of the form factors, in particular of the charge and magnetization radii provide strong tests for theory in the non-perturbative regime of QCD. However, the existing data at Q^2 below 1 (GeV/c)^2 are not precise enough for a hard test of theoretical predictions.rnrnFor a more precise determination of the form factors, within this work more than 1400 cross sections of the reaction H(e,e′)p were measured at the Mainz Microtron MAMI using the 3-spectrometer-facility of the A1-collaboration. The data were taken in three periods in the years 2006 and 2007 using beam energies of 180, 315, 450, 585, 720 and 855 MeV. They cover the Q^2 region from 0.004 to 1 (GeV/c)^2 with counting rate uncertainties below 0.2% for most of the data points. The relative luminosity of the measurements was determined using one of the spectrometers as a luminosity monitor. The overlapping acceptances of the measurements maximize the internal redundancy of the data and allow, together with several additions to the standard experimental setup, for tight control of systematic uncertainties.rnTo account for the radiative processes, an event generator was developed and implemented in the simulation package of the analysis software which works without peaking approximation by explicitly calculating the Bethe-Heitler and Born Feynman diagrams for each event.rnTo separate the form factors and to determine the radii, the data were analyzed by fitting a wide selection of form factor models directly to the measured cross sections. These fits also determined the absolute normalization of the different data subsets. The validity of this method was tested with extensive simulations. The results were compared to an extraction via the standard Rosenbluth technique.rnrnThe dip structure in G_E that was seen in the analysis of the previous world data shows up in a modified form. When compared to the standard-dipole form factor as a smooth curve, the extracted G_E exhibits a strong change of the slope around 0.1 (GeV/c)^2, and in the magnetic form factor a dip around 0.2 (GeV/c)^2 is found. This may be taken as indications for a pion cloud. For higher Q^2, the fits yield larger values for G_M than previous measurements, in agreement with form factor ratios from recent precise polarized measurements in the Q2 region up to 0.6 (GeV/c)^2.rnrnThe charge and magnetic rms radii are determined as rn⟨r_e⟩=0.879 ± 0.005(stat.) ± 0.004(syst.) ± 0.002(model) ± 0.004(group) fm,rn⟨r_m⟩=0.777 ± 0.013(stat.) ± 0.009(syst.) ± 0.005(model) ± 0.002(group) fm.rnThis charge radius is significantly larger than theoretical predictions and than the radius of the standard dipole. However, it is in agreement with earlier results measured at the Mainz linear accelerator and with determinations from Hydrogen Lamb shift measurements. The extracted magnetic radius is smaller than previous determinations and than the standard-dipole value.
Resumo:
Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn