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Register a new userCalculation of transport coefficient profiles in modulation experiments as an inverse problem
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The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusion model where these issues are related to the vanishing of the determinant of a 2x2 matrix. This sheds light on the accuracy of calculations with transport codes, and provides a path for a more precise assessment of the profiles and of the related uncertainty.
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The estimate of coefficients of the Convection-Diffusion Equation (CDE) from experimental measurements belongs in the category of inverse problems, which are known to come with issues of ill-conditioning or singularity. Here we concentrate on a particular class that can be reduced to a linear algebraic problem, with explicit solution. Ill-conditioning of the problem corresponds to the vanishing of one eigenvalue of the matrix to be inverted. The comparison with algorithms based upon matching experimental data against numerical integration of the CDE sheds light on the accuracy of the parameter estimation procedures, and suggests a path for a more precise assessment of the profiles and of the related uncertainty. Several instances of the implementation of the algorithm to real data are presented.
Assigning homogeneous boundary conditions, such as acoustic impedance, to the thermoviscous wave equations (TWE) derived by transforming the linearized Navier-Stokes equations (LNSE) to the frequency domain yields a so-called Helmholtz solver, whose output is a discrete set of complex eigenfunction and eigenvalue pairs. The proposed method -- the inverse Helmholtz solver (iHS) -- reverses such procedure by returning the value of acoustic impedance at one or more unknown impedance boundaries (IBs) of a given domain via spatial integration of the TWE for a given real-valued frequency with assigned conditions on other boundaries. The iHS procedure is applied to a second-order spatial discretization of the TWEs derived on an unstructured grid with staggered grid arrangement. The momentum equation only is extended to the center of each IB face where pressure and velocity components are co-located and treated as unknowns. One closure condition considered for the iHS is the assignment of the surface gradient of pressure phase over the IBs, corresponding to assigning the shape of the acoustic waveform at the IB. The iHS procedure is carried out independently for each frequency in order to return the complete broadband complex impedance distribution at the IBs in any desired frequency range. The iHS approach is first validated against Rotts theory for both inviscid and viscous, rectangular and circular ducts. The impedance of a geometrically complex toy cavity is then reconstructed and verified against companion full compressible unstructured Navier-Stokes simulations resolving the cavity geometry and one-dimensional impedance test tube calculations based on time-domain impedance boundary conditions (TDIBC). The iHS methodology is also shown to capture thermoacoustic effects, with reconstructed impedance values quantitatively in agreement with thermoacoustic growth rates.
We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4-6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron-ion coupling, inter-ion diffusion, ion viscosity, and charged particle stopping powers. Here, we give general background on Coulomb coupling and computational expense, review where some transport coefficients appear in hydrodynamic equations, and present the submitted data. Large variations are found when either the relevant Coulomb coupling parameter is large or computational expense causes difficulties. Understanding the general accuracy and uncertainty associated with such transport coefficients is important for quantifying errors in hydrodynamic simulations of inertial confinement fusion and high-energy density experiments.
We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured and the phase is not measured. The spatially distributed refractive index is the subject of the interest in this problem. Applications of this problem are in imaging of nanostructures and biological cells.
We investigate the jet quenching parameter in the case of a fast moving quark in an anisotropic plasma. In the leading log approximation, strong indications are found that the transport coefficient increases with increasing anisotropy. Implications for the phenomenology at RHIC are discussed.
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