Prediction of Fatigue Life in Plain Concrete Using Entropy Production

An energy approach within the framework of thermodynamics is used to model the fatigue process in plain concrete. Fatigue crack growth is an irreversible process associated with an irreversible entropy gain. A closed-form expression for entropy generated during fatigue in terms of energy dissipated is derived using principles of dimensional analysis and self-similarity. An increase in compliance is considered as a measure of damage accumulated during fatigue. The entropy at final fatigue failure is shown to be independent of loading and geometry and is proposed as a material property. A relationship between energy dissipated and number of cycles of fatigue loading is obtained. (C) 2015 American Society of Civil Engineers.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Synthesis and electron microscopy of high entropy alloy nanoparticles

This work provides a methodology for synthesizing isolated multi-component, high entropy alloy nanoparticles. Wet chemical synthesis technique was used to synthesis NiFeCrCuCo nanoparticles. As synthesized nanoparticles were spherical with an average size of 26.7 +/- 3.3 nm. Average composition of the as-synthesized nanoparticle dispersion was 26 +/- 2 at% Cr, 14 +/- 2 at% Fe, 10 +/- 0.6 at% Co, 25 +/- 0.1 at% Ni and 25 +/- 1.1 at% Cu. Compositional analysis of the nanoparticles conducted using the compositional line profile analysis and compositional mapping on a single nanoparticle level revealed a fairly uniform distribution of all the five component elements within the nanoparticle volume. Electron diffraction analysis clearly revealed that the structure of as-synthesized nanoparticles was face centered cubic. (C) 2015 Elsevier B.V. All rights reserved.

Bimodality and re-entrant behaviour in the hierarchical self-assembly of polymeric nanoparticles

We show that a film of a suspension of polymer grafted nanoparticles on a liquid substrate can be employed to create two-dimensional nanostructures with a remarkable variation in the pattern length scales. The presented experiments also reveal the emergence of concentration-dependent bimodal patterns as well as re-entrant behaviour that involves length scales due to dewetting and compositional instabilities. The experimental observations are explained through a gradient dynamics model consisting of coupled evolution equations for the height of the suspension film and the concentration of polymer. Using a Flory-Huggins free energy functional for the polymer solution, we show in a linear stability analysis that the thin film undergoes dewetting and/or compositional instabilities depending on the concentration of the polymer in the solution. We argue that the formation via `hierarchical self-assembly' of various functional nanostructures observed in different systems can be explained as resulting from such an interplay of instabilities.

Entropy Constrained Exemplar-based Image Inpainting

Image inpainting is the process of filling the unwanted region in an image marked by the user. It is used for restoring old paintings and photographs, removal of red eyes from pictures, etc. In this paper, we propose an efficient inpainting algorithm which takes care of false edge propagation. We use the classical exemplar based technique to find out the priority term for each patch. To ensure that the edge content of the nearest neighbor patch found by minimizing L-2 distance between patches, we impose an additional constraint that the entropy of the patches be similar. Entropy of the patch acts as a good measure of edge content. Additionally, we fill the image by considering overlapping patches to ensure smoothness in the output. We use structural similarity index as the measure of similarity between ground truth and inpainted image. The results of the proposed approach on a number of examples on real and synthetic images show the effectiveness of our algorithm in removing objects and thin scratches or text written on image. It is also shown that the proposed approach is robust to the shape of the manually selected target. Our results compare favorably to those obtained by existing techniques

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Exceptional resistance to grain growth in nanocrystalline CoCrFeNi high entropy alloy at high homologous temperatures

Nanocrystalline CoCrFeNi high entropy alloy, synthesized by mechanical alloying followed by spark plasma sintering, demonstrated extremely sluggish grain growth even at very high homologous temperature of 0.68 T-m (900 degrees C) for annealing duration of 600 h. Mechanically alloyed powder had carbon and oxygen as impurities, which in turn led to the formation of two-phase mixture of FCC and Cr-rich carbide with fine distribution of Cr-rich oxide during spark plasma sintering. Sluggish grain growth is attributed to the Zener pinning effect from the fine dispersion of oxide, mutual retardation of grain boundaries in the presence of two phases, and sluggish diffusivity because of cooperative diffusion of multi-principle elements. (C) 2015 Elsevier B.V. All rights reserved.

Nanoparticle induced miscibility in LCST polymer blends: critically assessing the enthalpic and entropic effects

The use of copolymer and polymer blends widened the possibility of creating materials with multilayered architectures. Hierarchical polymer systems with a wide array of micro and nanostructures are generated by thermally induced phase separation (TIPS) in partially miscible polymer blends. Various parameters like the interaction between the polymers, concentration, solvent/non-solvent ratio, and quenching temperature have to be optimized to obtain these micro/nanophase structures. Alternatively, the addition of nanoparticles is another strategy to design materials with desired hetero-phase structures. The dynamics of the polymer nanocomposite depends on the statistical ordering of polymers around the nanoparticle, which is dependent on the shape of the nanoparticle. The entropic loss due to deformation of polymer chains, like the repulsive interactions due to coiling and the attractive interactions in the case of swelling has been highlighted in this perspective article. The dissipative particle dynamics has been discussed and is correlated with the molecular dynamics simulation in the case of polymer blends. The Cahn Hillard Cook model on variedly shaped immobile fillers has shown difference in the propagation of the composition wave. The nanoparticle shape has a contributing effect on the polymer particle interaction, which can change the miscibility window in the case of these phase separating polymer blends. Quantitative information on the effect of spherical particles on the demixing temperature is well established and further modified to explain the percolation of rod shaped particles in the polymer blends. These models correlate well with the experimental observations in context to the dynamics induced by the nanoparticle in the demixing behavior of the polymer blend. The miscibility of the LCST polymer blend depends on the enthalpic factors like the specific interaction between the components, and the solubility product and the entropic losses occurring due to the formation of any favorable interactions. Hence, it is essential to assess the entropic and enthalpic interactions induced by the nanoparticles independently. The addition of nanoparticles creates heterogeneity in the polymer phase it is localized. This can be observed as an alteration in the relaxation behavior of the polymer. This changes the demixing behavior and the interaction parameter between the polymers. The compositional changes induced due to the incorporation of nanoparticles are also attributed as a reason for the altered demixing temperature. The particle shape anisotropy causes a direction dependent depletion, which changes the phase behavior of the blend. The polymer-grafted nanoparticles with varying grafting density show tremendous variation in the miscibility of the blend. The stretching of the polymer chains grafted on the nanoparticles causes an entropy penalty in the polymer blend. A comparative study on the different shaped particles is not available up to date for understanding these aspects. Hence, we have juxtaposed the various computational studies on nanoparticle dynamics, the shape effect of NPs on homopolymers and also the cases of various polymer blends without nanoparticles to sketch a complete picture on the effect of various particles on the miscibility of LCST blends.

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles

To improve the spatial distribution of nano particles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polymer chain dynamics in the vicinity of the nanoparticles. The effect of one-dimensional rodlike multiwall carbon nanotubes (MWNTs), with the characteristic dimension of the order of the radius of gyration of the polymeric chain, on the phase miscibility and chain dynamics in a classical LCST mixture of polystyrene/ poly(vinyl methyl ether) (PS/PVME) was examined in detail using the above techniques. In order to tune the localization of the nanotubes, different molecular weights of PS (13, 31, and 46 kDa), synthesized using RAFT (reversible addition fragmentation chain transfer) polymerization, was grafted onto MWNTs in situ. The thermodynamic miscibility in the blends was assessed by low-amplitude isochronal temperature sweeps, the spatial distribution of MWNTs in the blends was evaluated by PFQNM, and the hierarchical polymer chain dynamics was studied by DRS. It was observed that the miscibility, concentration fluctuation, and cooperative relaxations of the PS/PVME blends are strongly governed by the spatial distribution of MWNTs in the blends. These findings should help guide theories and simulations of hierarchical chain dynamics in LCST mixtures containing rodlike nanoparticles.

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles

To improve the spatial distribution of nano particles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polymer chain dynamics in the vicinity of the nanoparticles. The effect of one-dimensional rodlike multiwall carbon nanotubes (MWNTs), with the characteristic dimension of the order of the radius of gyration of the polymeric chain, on the phase miscibility and chain dynamics in a classical LCST mixture of polystyrene/ poly(vinyl methyl ether) (PS/PVME) was examined in detail using the above techniques. In order to tune the localization of the nanotubes, different molecular weights of PS (13, 31, and 46 kDa), synthesized using RAFT (reversible addition fragmentation chain transfer) polymerization, was grafted onto MWNTs in situ. The thermodynamic miscibility in the blends was assessed by low-amplitude isochronal temperature sweeps, the spatial distribution of MWNTs in the blends was evaluated by PFQNM, and the hierarchical polymer chain dynamics was studied by DRS. It was observed that the miscibility, concentration fluctuation, and cooperative relaxations of the PS/PVME blends are strongly governed by the spatial distribution of MWNTs in the blends. These findings should help guide theories and simulations of hierarchical chain dynamics in LCST mixtures containing rodlike nanoparticles.