Abstract:
A theoretical approach is developed for solving for the Reynolds stress in turbulent flows, and is validated for canonical flow geometries (flow over a flat plate, rectangular channel flow, and free turbulent jet). The theory is based on the turbulence momentum equation cast in a coordinate frame moving with the mean flow. The formulation leads to an ordinary differential equation for the Reynolds stress, which can either be integrated to provide parameterization in terms of turbulence parameters or can be solved numerically for closure in simple geometries. Results thus far indicate that the good agreement between the current theoretical and experimental/DNS (direct numerical simulation) data is not a fortuitous coincidence, and in the least it works quite well in sensible ways in canonical flow geometries. A closed-form solution for the Reynolds stress is found in terms of the root variables, such as the mean velocity, velocity gradient, turbulence kinetic energy and a viscous term. The form of the solution also provides radically new insight on how the Reynolds stress is generated and distributed.

Abstract:
In the title compound, {[NaTb(C7H6NO2)4(H2O)2]·C2H5OH·H2O}n, the TbIII atom is eight-coordinated in a slightly distorted square-antiprismatic geometry defined by four carboxylate O atoms and four pyridine N atoms. The bond lengths lie within the range 2.3000 (2)–2.326 (2) for the Tb—O bonds and 2.543 (3)–2.553 (3) for the Tb—N bonds. The NaI atom is five-coordinated by two water O atoms and three carboxylate O atoms in a distorted square-pyramidal geometry. In the crystal, intermolecular O—H...O hydrogen bonds link the molecules into a three-dimensional network.

Abstract:
In the title compound, C11H16N2O4, the 2,5-dimethoxyphenyl moiety is almost planar, with an r.m.s. deviation of 0.026 . The dihedral angle between the benzene ring and the plane of the urea moiety is 13.86 (5)°. The molecular structure is stabilized by a short intramolecular N—H...O hydrogen bond. In the crystal, intermolecular N—H...O and O—H...O hydrogen bonds link the molecules into a three-dimensional network.

Abstract:
In the title compound, C15H14F2N2O3, the dihedral angle between the benzene rings is 64.5 (1)°. One F atom is disordered over two meta positions, with occupancy factors of 0.72 and 0.28. In the crystal, molecules are linked by N—H...O hydrogen bonds involving two N—H and one C=O groups of the urea central fragment, leading to a supramolecular chain along [011].

Abstract:
In the title amide, C16H15F2NO4, the dihedral angle between the benzene rings is 2.33 (15)°. Molecules are linked in the crystal structure by N—H...O hydrogen bonding involving N—H and C=O groups of the amide function, leading to a supramolecular chain along [100].

Abstract:
The fast-growing field of soft matter research requires increasingly sophisticated tools for experimental studies. One of the oldest and most widely used tools to study soft matter systems is optical microscopy. Recent advances in optical microscopy techniques have resulted in a vast body of new experimental results and discoveries. New imaging modalities, such as nonlinear optical microscopy techniques that were developed to achieve higher resolution, enable soft matter research at length scales ranging from the molecular to the macroscopic. The aim of this chapter is to introduce a variety of optical microscopy techniques available to soft matter researchers, starting from basic principles and finishing with a discussion of the most advanced microscopy systems. We describe traditional imaging techniques, such as bright field and polarizing microscopy, along with state-of-the-art three-dimensional (3D) imaging techniques, such as fluorescence confocal and nonlinear optical microscopies. Different approaches are discussed along with their applications in the study of soft matter systems by providing typical examples.

Abstract:
We demonstrate orientation-sensitive multimodal nonlinear optical polarizing microscopy capable of probing orientational, polar, and biaxial features of mesomorphic ordering in soft matter. This technique achieves simultaneous imaging in broadband coherent anti-Stokes Raman scattering, multi-photon excitation fluorescence, and multi-harmonic generation polarizing microscopy modes and is based on the use of a single femtosecond laser and a photonic crystal fiber as sources of the probing light. We show the viability of this technique for mapping of three dimensional patterns of molecular orientations and that images obtained in different microscopy modes are consistent with each other.

Abstract:
The classical inverse optimization methodology for linear optimization assumes a given solution is a candidate to be optimal. Real data, however, is imperfect and noisy: there is no guarantee that a given solution is optimal for any cost vector. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization consisting of a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is in general nonconvex, we derive a closed-form solution and present the corresponding geometric intuition. Our goodness-of-fit metric, $\rho$, termed the coefficient of complementarity, has similar properties to $R^2$ from regression and is quasiconvex in the input data, leading to an intuitive geometric interpretation. We derive a lower bound for $\rho$ that possesses the same properties but is more tractable. We demonstrate the application of our framework for model estimation and evaluation in production planning and cancer therapy.

Abstract:
In the title compound, [Zn(CH3COO)2(C6H16N2)], the ZnII atom is coordinated by two N atoms of one bidentate diethylethylenediamine ligand and two O atoms of two acetate anions in a distorted tetrahedral geometry. The acetate ligands are asymmetrically coordinated to the Zn atom with two different C—O distances of 1.234 (4) and 1.275 (4) . The dihedral angle between the N/Zn/N and O/Zn/O planes is 83.11 (8)°. There are two independent molecules in the asymmetric unit. N—H...O hydrogen bonding links molecules into a three-dimensional network.

Abstract:
We develop an integrated system of holographic optical trapping and multimodal nonlinear microscopy and perform simultaneous three-dimensional optical manipulation and non-invasive structural imaging of composite soft-matter systems. We combine different nonlinear microscopy techniques such as coherent anti-Stokes Raman scattering, multi-photon excitation fluorescence and multi-harmonic generation, and use them for visualization of long-range molecular order in soft materials by means of their polarized excitation and detection. The combined system enables us to accomplish both, manipulation in composite soft materials such as colloidal inclusions in liquid crystals as well as imaging of each separate constituents of the composite material in different nonlinear optical modalities. We also demonstrate optical generation and control of topological defects and simultaneous reconstruction of their three-dimensional long-range molecular orientational patterns from the nonlinear optical images.