Browse Technical Reports - Theoretical and Applied Mechanics (TAM) by Title

  • Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2005-04)
    Using a nonstandard version of the principle of virtual power, we develop a gradient theory for incompressible flows at small length scales. In addition to a generalization of the Navier–Stokes equations involving higher-order ...

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  • Pushkin, Dmitri O.; Aref, Hassan (Department of Theoretical and Applied Mechanics (UIUC), 2001-07)
    A theory of stationary particle size distributions in coagulating systems with particle injection at small sizes is constructed. The size distributions have the form of power laws. Under rather general assumptions, the ...

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  • Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-06)
    We present a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing liquid crystal. These equations include a supplemental interface condition which expresses the ...

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  • Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2003-12)
    We derive a supplemental evolution equation for an interface between the nematic and isotropic phases of a liquid crystal when flow is neglected. Our approach is based on the notion of configurational force. As an application, ...

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  • Chaïeb, Sahraoui; Sato-Matsuo, Eriko; Tanaka, Toyoichi (Department of Theoretical and Applied Mechanics (UIUC), 2000-07)
    Polymer gels can undergo a volume phase transition (either continuous or discontinuous) when an external condition such as temperature or solvent composition is altered. This phase transition is either a shrinking or a ...

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  • Fried, Eliot; Sellers, Shaun (Department of Theoretical and Applied Mechanics (UIUC), 2005-09)
    The occurrence of striped domains in stretched nematic elastomers has been suggested as evidence for soft elasticity. Conversely, the neo-classical model of Bladon, Terentjev and Warner, which displays soft elasticity, ...

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  • Adrian, Ronald J.; Balachandar, S.; Liu, Zi-Chao (Department of Theoretical and Applied Mechanics (UIUC), 2001-09)
    Recent studies of the structure of wall turbulence have lead to the development of a conceptual model that validates and integrates many elements of previous models into a relatively simple picture based on self-assembling ...

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  • Tomkins, Christopher D.; Adrian, Ronald J. (Department of Theoretical and Applied Mechanics (UIUC), 2002-08)
    Spanwise structure and growth mechanisms in a turbulent boundary layer are investigated experimentally. PIV measurements are obtained in the streamwise–spanwise (x–z) plane from the buffer layer to the top of the logarithmic ...

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  • Natrajan, Vinay K.; Wu, Yanhua; Christensen, Kenneth T. (Department of Theoretical and Applied Mechanics (UIUC), 2006-04)
    The spatial signatures of retrograde spanwise vortices in wall turbulence are assessed from particle-image velocimetry measurements in the streamwise–wall-normal plane of a zero-pressure-gradient turbulent boundary layer ...

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  • Kasimov, Aslan R.; Stewart, D. Scott (Department of Theoretical and Applied Mechanics (UIUC), 2001-10)
    We investigate hydrodynamic instability of a steady planar detonation wave propagating in a circular tube to three-dimensional linear perturbations, using the normal mode approach. Spinning instability is identified and ...

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  • Chen, Xuemei; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-03)
    We consider the RayleighTaylor problem with a phase transformation. For simplicity, we restrict our attention to base states in which the interface convects with the phases, so that mass exchange between the phases occurs ...

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  • Dong, Fei; Hsui, Albert T.; Riahi, Daniel N. (Department of Theoretical and Applied Mechanics (UIUC), 2001-01)
    Linear and nonlinear analyses of thermal convection with a variable "buoyancy factor", which is defined as the product of thermal expansion coefficient and gravitational acceleration, are investigated for a fluid layer ...

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  • Shklyaev, Oleg E.; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-06)
    We use a newly developed set of boundary conditions to revisit the problem of an evaporating thin liquid film. In particular, instead of the conventional Hertz–Knudsen–Langmuir equation for the evaporation mass flux we ...

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  • Natrajan, Vinay K.; Yamaguchi, Eiichiro; Christensen, Kenneth T. (Department of Theoretical and Applied Mechanics (UIUC), 2006-04)
    Microscopic particle-image velocimetry (micro-PIV) measurements are made in the streamwise–wall-normal plane of a 536-micron capillary at Re = 4500 to study the statistical and structural features of wall turbulence at the ...

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  • Riahi, Daniel N. (Department of Theoretical and Applied Mechanics (UIUC), 2004-03)
    Steady and oscillatory modes of convective flow in a horizontal mushy layer during alloy solidification are reviewed. The theoretical problem has been based on the model developed by Amberg and Homsy and under the limit ...

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  • Fried, Eliot; Korchagin, Vladimir A. (Department of Theoretical and Applied Mechanics (UIUC), 2001-08)
    We consider a recent experiment of Kundler and Finkelmann (1995), who subjected an aligned specimen of nematic elastomer to uniaxial extension and observed the formation of striped domains. Working with an energy density ...

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  • Hill, Kimberly M.; Gioia, Gustavo; Tota, Vinay V. (Department of Theoretical and Applied Mechanics (UIUC), 2003-08)
    We show that the structure of a dense, free-surface boundary layer granular flow is similar to the structure of a laminar liquid flow: there is a strong component of order (stratification parallel to the mean flow) ...

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  • Gioia, Gustavo; Dai, Xiangyu (Department of Theoretical and Applied Mechanics (UIUC), 2005-08)
    Very recent experiments indicate that in free-standing metallic films of constant grain size the initial yield stress increases as the film becomes thinner, it peaks for a thickness on the order of 100 nm, and then starts ...

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  • Fried, Eliot; Gurtin, Morton E.; Shen, Amy Q. (Department of Theoretical and Applied Mechanics (UIUC), 2005-09)
    We develop a complete set of equations governing the evolution of a sharp interface separating a volatile-solvent/nonvolatile-surfactant solution from a vapor atmosphere. In addition to a sorption isotherm equation and the ...

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  • Stewart, D. Scott; Kasimov, Aslan R. (Department of Theoretical and Applied Mechanics (UIUC), 2004-10)
    We address the problem of generalizing sonic conditions to a three-dimensional unsteady self-sustained detonation wave. The conditions are shown to be the characteristic compatibility conditions on the exceptional surface ...

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