etd@IISc Collection:
http://hdl.handle.net/2005/42
2016-05-30T17:17:37ZMesophases Of Active Matter : Translational Order, Critical Rheology And Electrostatics
http://hdl.handle.net/2005/2519
Title: Mesophases Of Active Matter : Translational Order, Critical Rheology And Electrostatics
Authors: Adhyapak, Tapan Chandra
Abstract: This thesis consists of research work in the broad area of soft condensed matter theory with a focus on active matter. The study of long wavelength, low frequency collective behavior of active particles (bacterial suspensions, fish schools, motor-microtubule extracts, active gels) forms an interesting modification to liquid-crystal hydrodynamics, in which the constituent particles carry permanent stresses that stir the fluid. Activity introduces novel instabilities and many novel aspects emerge. Our works focus on the dynamics, order, fluctuations and instabilities in these systems. In particular, we investigated the dynamics, order and fluctuation properties emerging from effective hydrodynamic descriptions of translationally ordered active matter and also studied those in microwave-driven quantum Hall nematics. We also investigated the rheological properties of active suspensions subjected to an applied orienting field. A summary of the works carried out is as follows.
Translationally ordered active phases – active smectics and active cholesterics: Active or self-propelled particles consume and dissipate energy generating permanent stresses that stir the fluid around them. The collective behavior of systems of active particles, in systems with translational order, pose interesting questions and possibilities of new physics that differ strikingly from those in systems at thermal equilibrium with the same spatial symmetry. We developed the hydrodynamic equations of motion for (a) an active system with spontaneously broken translational symmetry in one direction, i.e., smectic and (b) the simplest uniaxially ordered phase of active chiral objects, namely, an active cholesteric. We analyze the fluctuation properties as well as the nature of characteristic instabilities that these systems can display and make a number of predictions. For example, in the case of an active smectic, we show that active stresses generate an effective active layer tension which, if positive, sup-presses the Landau-Peierls effect, leading to long-range smectic order in dimension d =3 and quasi-long-range in d =2, in sharp contrast with thermal equilibrium systems. Negative active layer tension in bulk systems, however, lead to a spontaneous Helfrich-Hurault undulation instability of the layers, accompanied by spontaneous flow. Also, active smectics, unlike orientationally ordered active systems, normally have finite concentration fluctuations. Similarly, for the case of cholesterics we show that cholesteric elasticity intervenes to suppress some of the instabilities present in active nematics.
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Numerical simulation of active smectics: We present results from a Brownian Dynamics simulation, with no hydrodynamic interaction, of a system of apolar active particles form-ing translational liquid-crystalline order in a suspension. The particles interact through a prolate-ellipsoidal Gay-Berne potential. We model activity minimally through different noise temperatures for movement along and normal to the orientation axis of each particle. We present preliminary results on the disruptive effect of activity on smectic order for the parameter values investigated. Future work will test the predictions of our theory [1] on active smectics.
Rheology of active suspensions near field-induced critical points : Shear induces orientation of active stresses in a suspension, through flow alignment. Depending on the sign, activity then either enhances or reduces the viscosity. The change in viscosity, in the zero frequency limit, is proportional to the product of the magnitude of active stress and the system relaxation time. A strong enough orienting field can make the system approach a critical point and the relaxation time diverges. We show that, this results in the divergence of viscosity at zero frequency making the system strongly viscoelastic. Depending on the sign, activity strengthens or reduces the effect of the field. We also investigate the rheological property of an active suspension with mixed polar and nematic oreder.
Active quantum Hall systems: We construct the hydrodynamic theory for a 2d charged active nematic with 3d electrostatics. We have investigated the interplay of the Coulomb interaction and activity in these systems. We show that activity competes to enhance the charge density fluctuations normally suppressed by long-ranged Coulomb interactions. The charge structure factor Sq of the corresponding passive charged nematic goes to zero as q, whereas in charged active nematics, activity leads to a nonvanishing charge structure factor at small wavenumber. We also show how the effect of an applied magnetic field can be incorporated into the dynamics of the system and leave scope for further studies on these effects.2016-04-25T18:30:00ZProlate Shaped Dark Matter Halo And The Galactic Warp
http://hdl.handle.net/2005/2522
Title: Prolate Shaped Dark Matter Halo And The Galactic Warp
Authors: Rahul Nath, R
Abstract: The physical explanation for the existence of the galactic warp is one of the major research areas in Astronomy. People have proposed various theories but nobody has yet given a convincing explanation. Most of the spiral galaxies are observed to be warped which reveals that the galactic warp is a stable characteristic. In the theory of kinematic bending wave, warp is considered as a wave that is propagated through the galactic disk with a speed called pattern speed.
If the pattern initially had straight line of nodes, according to bending wave theory, the warp would tend to wind up rapidly in the gravitational field of galactic disk. But still we observe warped galaxies in the sky. In the literature, it has been claimed that the winding problem of galactic warp may be solved by incorporating the effect of gravitational field of the dark matter halo in which the galactic disk is embedded. Recently some works on the dynamics of galactic disk claim that the shape of the dark matter halo is pro late spheroid. In this thesis, the effect of the gravitational field of a prolate spheroidal dark matter halo with varying eccentricity to the galactic warp is calculated and discussed.
Chapter1 gives the general introduction of the topics discussed in the following chapters. The structure of the spiral galaxy, their classifications, and the disk dynamics are discussed in the first few sections. One of the revolutionary concepts that emerged in the previous century was the existence of the dark matter. Presently tracing the mass distribution and the constituent particles of dark matter is one of the major research areas in theoretical and experimental physics. In this thesis, the effect of a particular type of mass distribution in dark matter halo on the warp is discussed in detail.
In the next few sections, the following topics are discussed namely; how the concept of dark matter came into astrophysics, how to measure the total mass inside a given radius and what are the different distributions used for various purposes. A new theory called Modified Newtonian Mechanism was also proposed in the previous century as an alternative to the dark matter concept which is also discussed briefly. Kinematic bending wave theory and the winding problem of the galactic warp is also discussed in detail. In the last section a relation between the pattern speed of the warp and the shape of the dark matter halo is obtained.
The calculation of the potential of a prolate spheroidal mass distribution with varying eccentricity is not done in any literature as we know. The calculation of the potential and the patten speed of prolate spheroidal mass distributions and of the galactic disk are described in chapter 2. The calculations of oblate spheroidal mass distribution are also discussed in this chapter but that is out of main theme.
In chapter 3 we apply the equations obtained in the Chapter 2 to one simple toy model and to the Galaxy. The rotation curve and the pattern speed of a warp in the gravitational ﬁeld of prolate spheroidal mass distribution of varying eccentricity are described. Usually the Milky Way disk is treated as an in infinitesimally thin disk but for our calculations the three dimensional but thin disk is used. The usually people use some approximation to calculate the potential due to galactic infinitesimal thin disk. The difference of the work from earlier works done by different people(with the approximation mentioned in above line) is also discussed in this Chapter. Chapter 4 discusses the summary of the entire work.2016-04-25T18:30:00ZConfinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding Systems
http://hdl.handle.net/2005/2502
Title: Confinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding Systems
Authors: Nandi, Saroj Kumar
Abstract: One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking.
Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion
of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis.
In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding.
In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters.
The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents.
In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases.
The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid.
When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials).
We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory.
In the final chapter, we summarize the problems studied in this thesis and point out some future directions.2016-02-16T18:30:00ZInvestigations Of Magnetic Anisotropy In Ferromagnetic Thin Films And Its Applications
http://hdl.handle.net/2005/2503
Title: Investigations Of Magnetic Anisotropy In Ferromagnetic Thin Films And Its Applications
Authors: Sakshath, S
Abstract: Physical systems having dimensions smaller than, or of the same order of magnitude as, the characteristic length scale relevant to a physical property are referred to as mesoscopic physical systems. Due to the dimensions of the system, several physical properties get affected and this could reveal interesting physics which would other-wise have not been apparent. In the recent times, a lot interesting applications have resulted from such studies.
The fundamental length scale in ferromagnetic systems is the exchange length. It is related to the magnetic anisotropy and exchange constants. Other length scales such as the size of a magnetic domain or a domain wall depends on the minimisation of energy associated with this length scale along with other factors such as zeeman energy, magnetostatic, magnetoelastic and anisotropy energies.
Ultrathin magnetic films have thickness smaller than the exchange length. In this thickness regime, the surface of the film plays an important role. The magnetic anisotropy energy would get a significant contribution from the surface of the film and if it dominates over the volume contribution, would eventually lead to magnetisation pointing out of the plane of the film as opposed to imposition of demagnetising fields. Examples for such cases are FePt(L10 phase) films and Co(0001) films. Such films are important in memory applications where perpendicularly magnetised recording media are desired. When the lateral dimensions of thin films are reduced, demagnetising fields become even more important. Depending on the anisotropy in the system, certain domain patterns get stabilised in the final structure. This has led to important applications in the field of magnonics. The use of angular momentum transfer from spin polarised electrons to change the configuration of magnetisation of structured magnetic films has led to interesting memory and oscillator applications. The underlying physical parameter that needs to be controlled and carefully studied in all these cases is the magnetic anisotropy. It is favourable to have uniaxial magnetic anisotropy for memory and oscillators. This thesis chiefly deals with Fe/GaAs(001) systems. The choice of the physical system follows interest in spintronics where spin injection is desired into a semiconductor from a ferromagnet. The thesis is organized into chapters as follows.
Chapter 1 attempts to introduce the reader to some of the basic concepts of mag-netism and some magnetic phenomena. The characteristic nature of a ferro-magnetic material is its spontaneous magnetisation due to long range ordering below the Curie temperature. But the moment is coupled, through some in-teractions, to spatial co-ordinates which leads to spatial variation of magnetic properties. Such interactions are also responsible for the formation of magnetic domains. The spatial variation of magnetic properties within a ferromagnet is called magnetic anisotropy. A major part of the thesis deals with the study of magnetic anisotropy of Fe thin films grown on GaAs(001) substrates. For a better understanding, the structure of the semiconductor is introduced first before discussing the influence of the structure of GaAs on the growth of Fe. A short description of the uniaxial magnetic anisotropy in Fe films is given before starting on an exploration of some possible reasons for it. Concepts of ferromagnetic resonance, spin torque eﬀect and micromagnetic simulations are given.
Chapter 2 gives a brief description of some of the experimental apparatus that was setup during the course of the research along with an overview of the diﬀer-ent sample preparation and characterisation techniques used. The chapter is organised according to the general functionality of the techniques. Some con-cepts such as the use of low energy electrons, nanostructuring etc are introduced along with the corresponding techniques since it is best understood along with the instrumentation.
Chapter 3 reports some surprising findings about the in-plane magnetic anisotropy in Fe films grown on an MgO underlayer. Until now, it has been understood that such films should exhibit only a four-fold magnetic anisotropy within the plane of the film. But the Fe/MgO/GaAs(001) films studied here exhibited an in-plane uniaxial magnetic anisotropy(IPUMA). IPUMA is dominant upto about 25 ML of Fe in case of Fe/MgO/GaAs(001) films whereas, in Fe/GaAs(001) films it is dominant only upto about 15 ML. Thus, the presence of the MgO film even appeared to enhance the uniaxial anisotropy as compared to the Fe/GaAs(001) films. In the ferromagnetic resonance (FMR) spectra, as many as three peaks were observed in Fe/GaAs(001) films of thickness 50 ML close to the hard axis of magnetisation. This means that three could be three energy minima possibly due to a competition between the anisotropies involved.
Chapter 4 elaborates the investigations of the eﬀect of orientation and doping con-centration of the GaAs substrate on the magnetic anisotropy of Fe/GaAs(001) films. It is found that doping the substrate (n type) reduces the strength of the IPUMA in Fe/GaAs films. In the wake of the long-standing debate of electronic structure v/s stress as the origin of the IPUMA in Ferromagnet/Semiconductor films, this result is important because it implies that the electronic structure of the Fe/GaAs interface influences the magnetic anisotropy. But stress, as a cause of IPUMA cannot be ruled out. The influence of deposition techniques on magnetic anisotropy is also investigated.
Chapter 5 presents a way of manipulating magnetic anisotropy, and hence mag-netisation dynamics, by nanostructuring of epitaxial Fe films. It is based on the property that magnetic anisotropy of Fe films is thickness dependent. It is demonstrated that using techniques of nanostructuring, a 2 dimensional mag-netic system with controllable variation of local magnetic anisotropy is created. Such a system could be a potential magnonic crystal.
chapter 6 demonstrates the proof of concept of a new memory device where memory is stored in the magnetic domain configuration of a ring in relation to that of a nano-wire. Switching between the memory states is acheived through spin trasfer torque of an electric current passing through the device, whereas read-out of the memory state is through the measurement of resistance of the device. Devices are made using NiFe and Co; it is seen that the behaviour of the devices can be explained taking into account the anisotropic magnetoresistance of the material used.
Finally, the various results are summarised and a broad outlook is given. Some possible future research related to the topics dealt within this thesis is discussed.2016-02-16T18:30:00Z