The interests of the researchers in the Working Group span a very wide range of topics. In order to maintain focus, three specific problems have been chosen to form the core of the research program, though other areas will continue to be explored.
It is important to point out that these three nonequilibrium applications are far from being exhaustive, even within the Laboratory. The topics chosen above have a particularly attractive cohesion with which to develop the LANL nonequilibrium competency. As a result of extensive discussions in our Working Group it is clear that several additional multiscale programs will directly benefit from, and can provide valuable input to, our program. In particular, we have recognized strong connections with research needs, and established interactions with leaders in: biophysics (H. Frauenfelder), materials deformation, processing, and advanced manufacturing (R. LeSar), and ocean dynamics modeling (L. Margolin). We will continue close interactions with these and other programs, make available to them progress in this thrust, and help guide LANL investment strategies.
As one example of a related effort, ocean circulations determine much of the long term variability of the earth's climate. The global ocean exhibits multiple equilibria of its large thermohaline circulations, spending long periods (millennia) in the neighborhood of one equilibrium, then undergoing a rapid transition to another. It is supposed that these transitions are triggered by fluctuations in the small scale dynamics. Present day computing resources fall short by many orders of magnitude from allowing fully resolved ocean simulations over periods of thousands of years. A coarse graining technique, based on nonlinear enslavement, has been developed by Margolin (XHM) and collaborators, and demonstrated in the context of models of ocean basin circulations. The need now is to develop a new class of multiscale models that include the effects of fluctuations by generalizing the method of nonlinear enslavement. The fluctuating part must be simulated as a stochastic process. The new mesoscale dynamical equations will have the form of the Navier-Stokes' equations, with a renormalized viscosity representing the dissipative effects of the unresolved scales, with an added noise term representing the effects of the fluctuations. Both the coarse graining methodology and stochastic PDEs are common elements with the rest of the nonequilibrium research program.
The three focus areas are:
Shock-induced transformations (phase transformations/melting induced by pressure, shock, or deformation) in metals are an excellent test-case for fundamental physics issues involving nonequilibrum phenomena as it is necessary to go beyond approaches based on the equation of state or thermodynamics. Issues characteristic of this problem are natural competitions among very disparate rates and the need for a spatial and temporal control of micro-meso-macro relationships.
Predictive models of dynamic materials response and other relevant physical processes are required to understand the complex shock and release conditions induced by high-explosive drives. Shock-induced phase transitions between different crystalline phases of a metal and the subsequent microstructure evolution during shock release are currently at the forefront of modeling requirements inasmuch as such processes are presently very poorly understood and yet the associated impact of changes in the internal energy, plastic constitutive behavior, and fracture dynamics is potentially of the utmost importance. Predictive models of shock-induced phase transitions are needed for implementation in hydrodynamic codes for simulations of dynamic deformation.
The shock process across an equilibrium phase boundary leaves the metal, in general, as an admixture of the two phases in a nonequilibrium state. One of our research objectives is the identification of the extended microstructural defects responsible for nucleating of displacive transformations in metals and alloys, particularly under shock-loading conditions, and the modeling of the nucleation process. The closely-related problem of the heterophase interface propagation and the cessation of its advance by mounting internal stresses will also be addressed. Predictive models of these important metallurgical processes would also benefit the steel industry.
Under extreme conditions of temperature (T_c = 200 Mev) and density (n_c = .2 \ fm^(-3)), a new phase of nuclear matter is produced, the quark-gluon plasma (QGP). These conditions will be achieved at the Relativistic Heavy Ion Collider (RHIC) at BNL and the Large Hadron Collider (LHC) at CERN. For these experimental programs it is vital to determine what are the special signatures (such as coherent production of particles and their correlations in momentum and rapidity) of this new state of matter.
The rapid expansion and cooling of the QGP produced in a relativistic heavy ion collision is clearly far from equilibrium, and is similar to the rapid quench of a magnet from its disordered phase to its ordered phase. During the nonequilibrium chiral phase transition domains aligned in different directions in isospin space can be formed which then decay coherently to pions, producing a ``pion laser.'' These domains are nonlinear coherent structures very much analogous to those produced in the shock induced transitions or high magnetic field applications. In all these cases the collective modes can be described by a Landau-Ginsburg theory. Because the pion emission is coherent the signature of pion ``lasing'' would be unusual (i.e. non-Poisson) statistics in the ratio of charged to neutral pions, particularly at low momentum. Experiments at RHIC such as PHENIX (P-25) will look for the predicted distortion of the pion spectrum which would be the first experimental evidence for the chiral/QGP phase transition and this new state of nuclear matter. As in the other applications, the challenge for the modeling is to incorporate the fluctuations of the small scale quark-gluon degrees of freedom of the microtheory (QCD) on the soft pionic states that are actually observed by the detector in a reliable and systematic way.
We will first determine and solve numerically the fluctuation moment hierarchy equations of the QGP from the fundamental microtheory, QCD. This will make possible the first detailed calculation of transport coefficients, damping rates, and energy loss characteristics of this new phase of matter from first principles. Having characterized the non-Gaussian spectrum and statistics of the microtheory, we will develop an effective transport theory for the more slowly varying coherent fields interacting with these fluctuations. We will be able to check and control the ``thinning'' of degrees of freedom and obtain numerically the dynamical equation of state of the QGP. Renormalization group methods and nonlinear enslavement algorithms will be employed at this step. Further iterations of this procedure with stringent analytic and numerical control at each stage will enable us to test the hydrodynamical models of the QGP. Our microscopic approach to the nonequilibrium QGP phase transition will provide a crucial, testable multiscale template for the more phenomenological descriptions of complex nonequilibrium processes and structures in the other applications.
Topological defects (vortices, dislocations, etc.) underly nonequilibrium morphology and evolution in many condensed matter and materials examples, from stress-strain relations in solids (as in the shock induced phase transitions above), to surface growth, magnets, and polymers. We will focus on flux structure and dynamics in superconductors which has long been a primary context for nonequilibrium phenomena, but largely on a phenomenological modeling basis. A deeper understanding is now urgently needed at LANL, because (a) totally new superconducting materials (including organic, high-T inorganic cuprate, and f-electron superconductors) are being explored (STC) for completely new application regimes (in motors, wires, electronics), and (b) the availability of unprecedented high magnetic fields at NHMFL. These fortunate LANL circumstances demand a new level of control of the nonequilibrium-nonlinear spatiotemporal responses and phase transformations, as functions of geometry, dimensionality, external fields (magnetic, electric), temperature and disorder. All applications rely on the nucleation and dynamics of specific intrinsic collective structures with respect to the superconducting condensate described by microscopic BCS theory: topological flux lines with characteristic core and far-field structures, closely analogous to dislocations in solids. All are topological excitations whose interactions determine mesoscopic order, controlling macroscopic strength, flow and failure (e.g. stress-strain and deformation in solids). In superconductors they determine the critical currents and dissipation, and hence all nonequilibrium transport and magneto-electro response properties. The necessary concepts, analytical techniques, and numerical strategies (see flow chart) are precisely those of other nonequilibrium situations discussed in this proposal, since they rest on the origins and nonequilibrium mesoscale properties of very similar coarse-grained time-dependent nonlinear Landau-Ginsburg free energy functionals.
We will use experimental data from LANL programs (STC, MST) and major facilities (NHMFL) to address the following frontier issues: (i) Plasma resonances and critical currents in high magnetic fields for highly anisotropic layered superconductors. Comparisons will be made with new high magnetic field plasma resonance data from LANL, Princeton and Tokyo. (ii) Vortex lattice ordering and melting transitions in the presence of temperature, external currents and disorder. We will model the intricate mesoscopic dynamical states as strong analogs of dislocation ordering into strain bands and nonlinear plastic flow regimes in solids. Detailed comparison with flux melting experiments will be made, including LANL studies of pinning and critical fields in the presence of columnar defects induced by ion-implantation (P-15). (iii) Metastable filamentary vortex flow in thin film superconductors, where the vortex-vortex interactions are far less screened and where long-range fields are essential. Very recent data (Stanford, Illinois) suggests that amorphous thin film superconductors exhibit ``stick-slip" instabilities.
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Salman Habib / T-8 / LANL / habib@lanl.gov / revised March 97