39,690 research outputs found
Tilt grain boundary instabilities in three dimensional lamellar patterns
We identify a finite wavenumber instability of a 90 tilt grain
boundary in three dimensional lamellar phases which is absent in two
dimensional configurations. Both a stability analysis of the slowly varying
amplitude or envelope equation for the boundary, and a direct numerical
solution of an order parameter model equation are presented. The instability
mode involves two dimensional perturbations of the planar base boundary, and is
suppressed for purely one dimensional perturbations. We find that both the most
unstable wavenumbers and their growth rate increase with , the
dimensionless distance away from threshold of the lamellar phase.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
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Experimental study on transcritical Rankine cycle (TRC) using CO2/R134a mixtures with various composition ratios for waste heat recovery from diesel engines
A carbon dioxide (CO2) based mixture was investigated as a promising solution to improve system performance and expand the condensation temperature range of a CO2 transcritical Rankine cycle (C-TRC). An experimental study of TRC using CO2/R134a mixtures was performed to recover waste heat of engine coolant and exhaust gas from a heavy-duty diesel engine. The main purpose of this study was to investigate experimentally the effect of the composition ratio of CO2/R134a mixtures on system performance. Four CO2/R134a mixtures with mass composition ratios of 0.85/0.15, 0.7/0.3, 0.6/0.4 and 0.4/0.6 were selected. The high temperature working fluid was expanded through an expansion valve and then no power was produced. Thus, current research focused on the analysis of measured operating parameters and heat exchanger performance. Heat transfer coefficients of various heat exchangers using supercritical CO2/R134a mixtures were provided and discussed. These data may provide useful reference for cycle optimization and heat exchanger design in application of CO2 mixtures. Finally, the potential of power output was estimated numerically. Assuming an expander efficiency of 0.7, the maximum estimations of net power output using CO2/R134a (0.85/0.15), CO2/R134a (0.7/0.3), CO2/R134a (0.6/0.4) and CO2/R134a (0.4/0.6) are 5.07 kW, 5.45 kW, 5.30 kW, and 4.41 kW, respectively. Along with the increase of R134a composition, the estimation of net power output, thermal efficiency and exergy efficiency increased at first and then decreased. CO2/R134a (0.7/0.3) achieved the maximum net power output at a high expansion inlet pressure, while CO2/R134a (0.6/0.4) behaves better at low pressure
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
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