Research interests:

My interests are my castle!

Rafi Blumenfeld: Research plans / main interests

The following list is in constant evolution. The highlighted words will send you to somewhat more detailed decriptions of the approaches that I take / intend to take / would like to take in addressing these problems. This page is updated rather slowly, but it gives a flavour of what I have been doing. Since the list covers a rather broad range of interests progress is limited to current pet problems. I therefore welcome discussions that may either result in collabotaions or get others involved in some of these ideas.

Current interests

Past interests

(Some of these are still lingering, with semi-developed ideas lying all around. I would love to finish exploring some of those ideas but am defeated by lack of time and resources. Assistance would be quite welcome.)

  • Protein dynamics
    A project on hold that has resulted in a rather efficient code for the dynamics of a protein-like curve in a fluid. We were very optimistic that we could revolutionise the field by producing a code that will effortlessly simulate the folding of proteins. Another ambitious target was to construct a good model for the dynamics of biological molecules in solutions. Such a model is very useful in many applications for, eg., the mobility of DNA molecules in electrophoresis, the drag mechanisms in low concentrations of polymer and the effects on viscosity. (Collaboration: M. Schwartz, Y. Navot)

  • fracture and crack propagation
    Slow cracking 1 2 3, fast cracking 1, and the rough surfaces that emerge 1 2. (Collaboration: B. L. Holian, R. C. Ball, P. Gumbsch).

  • Characterization of hierarchical and fractal patterns beyond simple scaling
    Most hierarchical and fractal structures are characterized by their so-called fractal dimension, aka the scaling index. Yet, many structures with very close or even identical fractal dimension look completely different. This direction consists of methods to characterise such differences systematically (Collaboration: Robin C. Ball, Benoit B. Mandelbrot and S. Torquato).

  • A first-principles statistical theory for evolving interfaces
    In the course of studying the paradigmatic model of diffusion-limited-aggregation I discovered an underlying Hamiltonian in the quasi-static problem. This means that one can apply statistical mechanical tools to investigate the statistics of the evolving patterns. Progress in this direction has been put on hold for lack of time and a sufficiently enthusiastic collaborator/student. (Collaboration: Robin C. Ball).

  • Properties of strongly nonlinear and inhomogeneous/textured media
    An old flame that is still silently burning. I have looked into quite a few problems involving such systems. Many of these involvde finding the macroscopic properties of media that respond in a strongly nonlinear fashion to an applied field, unlike the usual linear responses we learn in kindergarten, such as Ohm's law, a linear dielectric response to an electric field, or a linear stress-strain relation. Electrical examples of such systems are networks of varistors, where the voltage drop varies as a power law in the current. Mechanical examples are systems were the stress-strain or stress-strain rate relations are strongly nonlinear (e.g. in creep or nonlinear solids). I have then gone on to analyse what happens if such media are also geometrically disordered, namely, their constitutive properties vary significantly from point to point. Many of the results that I have obtained have been used by later researchers in the field (in fact some were rediscovered) but some have not, and there is still a great deal of exciting gems to mine, both in the theoretical and applied directions.

  • Electromagnetic waves in strongly nonlinear media
    I may elaborate on this part of my work if time ever permits. See e.g.,
    1. Nonlinear dielectrics: electrostatics of random media and propagation of waves in a homogeneous slab;
    2. Novel flux solutions in nonlinear continuum systems with negative dynamic resistance;
    3. Strongly nonlinear composite dielectrics: a method for exact solution for the potential field and effective bulk properties;
    4. An exact solution for electromagnetic waves in strongly nonlinear media .

Prof. Rafi Blumenfeld: Gonville and Caius College, Trinity St., Cambridge CB2 1TA, UK
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