Sarang gopalakrishnan thesis

Professor Robert Hilborn Recent experiments indicate that the sign and magnitude of synaptic changes in neurons depend on the relative timing of pre- and post-synaptic action potentials. This form of synaptic plasticity is called spike-timing-dependent plasticity or STDP.

Sarang gopalakrishnan thesis

Professor Robert Hilborn Recent experiments indicate that the sign and magnitude of synaptic changes in neurons depend on the relative timing of pre- and post-synaptic action potentials. This form of synaptic plasticity is called spike-timing-dependent plasticity or STDP.

The magnitude of STDP at a particular synapse can also depend on the strength of the synapse. For example, Sarang gopalakrishnan thesis certain systems strong synapses are strengthened less than weak synapses.

Changing the strength dependence can lead to a range of distributions, characterized by differing degrees of stability and inter-synaptic competition.

In this thesis I explore the consequences of various forms of STDP through computer simulations and through techniques from statistical mechanics, in particular, through the Fokker-Planck equation.

Jessie Erwin, '06 Faculty Advisor: Professor Robert Hilborn To function correctly, genetic networks depend upon a series of positive and negative regulatory proteins.

For the type of genetic oscillator in which we are interested, this genetic network controls circadian rhythm: This system can be modeled through two coupled differential equations describing the changes in the concentrations of a repressor protein and of an inactive complex formed from the binding of an activator and a repressor protein.

We wish to explore the consequences of adding noise of varying amplitudes into our genetic oscillator system to mimic the fluctuations in protein Sarang gopalakrishnan thesis and thermal fluctuations that occur in real cells.

Preliminary results suggest that certain amplitudes of noise can stimulate regular oscillations in genetic oscillators that have otherwise settled into a steady state. Professor Jonathan Friedman Molecular magnets stand between the realms of quantum and classical physics.

At first glance they exhibit the trademark behaviors of macroscopic magnets, such as bi-stability and hysteresis. But when the temperature is low enough to suppress the classical behavior i.

For example, the magnetic moment of the molecule can tunnel through a classically forbidden energy region. This quantum behavior is manifest because the individual ions in a molecular magnet are coupled together very strongly, and the entire molecule therefore behaves much like a single quantum entity of spin Despite the accuracy of such a quantum picture of the molecule, however, the large spin prevents much analytic progress from being made through a strictly quantum mechanical approach.

Instead, one must use semi-classical methods to explain the quantum behavior. The specific quantum effect that I will deal with in my thesis is the complete suppression of the tunneling rate between the ground states of MnAcetate due to variations in the parameters of the system's Hamiltonian with a fourth order perturbation that might be induced by mechanical pressure.

This quenching effect has been understood in a similar situation where the perturbation was given by a transverse magnetic field to be the result of the interference between various tunneling paths.

Sarang gopalakrishnan thesis

I will apply several semi-classical and approximate techniques which proved useful in the transverse field calculations in order to model the similar behavior of Mn12 under our Hamiltonian. When these domains are identical, H is said to be self-adjoint. It is sometimes possible to extend the domain of a non-self-adjoint H until it is self-adjoint.

I will study the technique of choosing self-adjoint extensions, and its relation to renormalization theory, chiefly in the context of two problems in nonrelativistic quantum mechanics, the 2-D delta function potential and the inverse-square potential.

A link between these problems is that both have classically scale-invariant potentials that acquire a scale upon quantization which depends on the self-adjoint extension that is chosen ; this feature is called "anomalous symmetry breaking" and is an important part of the symmetry structure of quantum mechanics.

A related topic, which I will study if time permits, is modifying quantum mechanics so that it has an intrinsic scale built into it, and the consequences of this for symmetries and self-adjointness. Ben Heidenreich, '06E Faculty Advisor: Professor Larry Hunter Symmetry has played an important role in the development of physics.

One symmetry of particular interest is reflection symmetry, often referred to as parity P invariance. Although this symmetry is obeyed in much of physics, the weak interaction, responsible for nuclear beta decay, is know to violate parity. My thesis deals with an analogous symmetry known as time reversal T invariance.

Events viewed in reverse order, such as when a video tape is played backwards, often appear bizarre. Shattered crockery reassembles without a crack, and rivers flows uphill. However, in some sense the time-reversed universe is fundamentally the same as our own.

Balls still bounce in the same way, and objects thrown in the air still follow parabolas. In fact, all the strange occurrences mentioned above are very unlikely to occur, but technically possible. In a fundamental sense, physical law is nearly completely T invariant.

Primary Research Area

At present, the only indication of fundamental T violation is the existence of certain decay modes of the neutral K and B mesons. Based on observations of these decays, some theories predict that the electron should have a nonzero electric dipole moment EDM.

To test these theories, we attempt to measure the electron EDM.Thesis: Transport and Wenbo Fu, Harvard University Thesis: The Sachdev-Ye-Kitaev model and matter without quasiparticles; Seth Whitsitt, Harvard University Thesis: Universal non-local observables at interacting quantum critical points; Sarang Gopalakrishnan, Assistant Professor, City University of New York; Andrea Allais, Cruise.

[email protected] Degrees/Diplomas: University of Illinois at Urbana-Champaign Research Interests: Theoretical condensed matter physics, Theoretical atomic and optical physics, Quantum information theory.

My thesis will be an investigation of the properties of single and binary 87 Rb Bose-Einstein condensates. The addition of a microwave synthesizer, amplifier, and delivery horn over the summer has allowed us to produce cold thermal clouds or condensates in the |F=1,m f =-1> spin state and transfer them to the |2,1> state.

With the aid of quickly reversible optical pumping we have also independently condensed |1,-1> . In this thesis, we use superconducting island arrays as a platform for studying vortex motion and quantum phase transitions.

Sarang Gopalakrishnan; View an early version of these results was pre- sented by one of the present authors 30 and has also ap- peared in the DPhil thesis of another Rahul Nandkishore: Combined Curriculum Vitae and List of Publications Employment Assistant Professor of Physics at the University of Colorado - Boulder, Boulder, Co, USA. August to present Postdoctoral fellow at the Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA. (September August ). Sarang Gopalakrishnan. PhD thesis: Photon-Mediated Emergent Phenomena in Optical Cavities; Completed his PhD in summer Left to begin a Harvard Quantum Optics Center Prize Postdoctoral Fellowship in the Department of Physics at Harvard University.

We investigate superconducting vortex dynamics and lattice structures in superconducting arrays by performing electrical transport measurements on Nb island arrays on Au at milli-kelvin temperatures and finite fields. Stephanie Law Toner and Matt Toner, Tomoki Ozawa, Wade DeGottardi, Sarang Gopalakrishnan, Seungmin Hong, and Rick and Kristen Moon.

None of this would have been possible without the love and support of my family. This "Cited by" count includes citations to the following articles in Scholar.

The ones marked * may be different from the article in the profile.

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