Ab Initio Studies of Cellulose I: Crystal Structure, Intermolecular Forces, and Interactions with Water

We have studied the structural, energetic, and electronic properties of crystalline cellulose I using first-principles density functional theory (DFT) with semiempirical dispersion corrections. The predicted crystal structures of both Iα and Iβ phases agree well with experiments and are greatly improved over those predicted by DFT within the local and semilocal density approximations. The cohesive energy is analyzed in terms of interchain and intersheet interactions, which are calculated to be of similar magnitude. Both hydrogen bonding and van der Waals (vdW) dispersion forces are found to be responsible for binding cellulose chains together. In particular, dispersion corrections prove to be indispensable in reproducing the equilibrium intersheet distance and binding strength; however, they do not improve the underestimated hydrogen bond length from DFT. The computed energy gaps of crystalline cellulose are 5.7 eV (Iα) and 5.4 eV (Iβ), whereas localized surface states appear within the gap for surfaces. The interaction of cellulose with water is studied by investigating the adsorption of a single water molecule on the hydrophobic Iβ(100) surface. The formation of hydrogen bond at the water/cellulose interface is shown to depend sensitively on the adsorption site for example above the equatorial hydroxyls or the CH moieties pointing out of the cellulose sheets. VdW dispersion interactions also contribute significantly to the adsorption energy

Relationship between Religion and Native American Identity

The purpose of this study was to determine whether there is a relationship between religious affiliation and Native American Identity. Based on the findings of this study, a component of a Native American\u27s Identity is their religious affiliation. To contribute to the research on Native American and Alaskan Native identity, this study targeted the teenage demographic of ages 12 to 19 years old. Over growing concern, expressed by tribal elders, about a loss of cultural identity amongst teens, this study investigates a connection between a teen’s sense of identity and their religious affiliation (Quigley, 2019). This study used a multiple-choice survey tool, that was filtered to only include Native American and Alaskan Native teens, where participants self-identified their cultural identity and their religious affiliation. This survey data comes from Swaim and Stanley (2021) who studied “substance use among American Indian youth” (Swaim & Stanley, 2021). The null hypothesis of this study is that religious affiliation has no effect on Native American Identity. The alternative hypothesis is that religious affiliation does influence Native American Identity. To test this cross tabulations and a Pearson’s R analysis were run. Further hypotheses were made concerning each religious preferences impact on Native American Identity. Another hypothesis was made that says not belonging to a religion reduces a person\u27s Native American Identity. To test these hypotheses simple regressions were run. This study concluded that there is a positive correlation between Traditional Native American Spirituality and high level Native American Identity. Incidentally there is a correlation between no religious affiliation and low level Native American Identity. Lastly a moderated regression was done to see if gender had a moderating effect on the relationship between religious preference and Native American Identity. This study found that gender did not have a moderating effect.https://scholarscompass.vcu.edu/gradposters/1168/thumbnail.jp

Power-law Schell-model Sources

A new type of Schell-model source is developed that has a spectral degree of coherence, or spatial power spectrum, which is described by a power-law function. These power-law sources generally produce cusped, or peaked far-zone spectral density patterns making them potentially useful in directed energy applications. The spectral degrees of coherence, spatial power spectra, and spatial coherence radii for power-law sources are derived and discussed. Two power-law sources are then synthesized in the laboratory using a liquid crystal spatial light modulator. The experimental spectral densities are compared to the corresponding theoretical predictions to serve as a proof of concept

Twisted Spatiotemporal Optical Vortex Random Fields

We present twisted spatiotemporal optical vortex (STOV) beams, which are partially coherent light sources that possess a coherent optical vortex and a random twist coupling their space and time dimensions. These beams have controllable partial coherence and transverse orbital angular momentum (OAM), which distinguishes them from the more common spatial vortex and twisted beams (known to carry longitudinal OAM) in the literature and should ultimately make them useful in applications such as optical communications and optical tweezing. We present the mathematical analysis of twisted STOV beams, deriving the mutual coherence function and linear and angular momentum densities. We simulate the synthesis of twisted STOV beams and investigate their free-space propagation characteristics. We discuss how to physically generate twisted STOV fields and lastly conclude with a summary and brief discussion of future research

The Behavior of Partially Coherent Twisted Space-time Beams in Atmospheric Turbulence

We study how atmospheric turbulence affects twisted space-time beams, which are non-stationary random optical fields whose space and time dimensions are coupled with a stochastic twist. Applying the extended Huygens–Fresnel principle, we derive the mutual coherence function of a twisted space-time beam after propagating a distance z through atmospheric turbulence of arbitrary strength. We specialize the result to derive the ensemble-averaged irradiance and discuss how turbulence affects the beam’s spatial size, pulse width, and space-time twist. Lastly, we generate, in simulation, twisted space-time beam field realizations and propagate them through atmospheric phase screens to validate our analysis

Stochastic Complex Transmittance Screens for Synthesizing General Partially Coherent Sources

We develop a method to synthesize any partially coherent source (PCS) with a genuine cross-spectral density (CSD) function using complex transmittance screens. Prior work concerning PCS synthesis with complex transmittance screens has focused on generating Schell-model (uniformly correlated) sources. Here, using the necessary and sufficient condition for a genuine CSD function, we derive an expression, in the form of a superposition integral, that produces stochastic complex screen realizations. The sample autocorrelation of the screens is equal to the complex correlation function of the desired PCS. We validate our work by generating, in simulation, three PCSs from the literature—none has ever been synthesized using stochastic screens before. Examining planar slices through the four-dimensional CSD functions, we find the simulated results to be in excellent agreement with theory, implying successful realization of all three PCSs. The technique presented herein adds to the existing literature concerning the generation of PCSs and can be physically implemented using a simple optical setup consisting of a laser, spatial light modulator, and spatial filter

Twisted Space-frequency and Space-time Partially Coherent Beams

We present partially coherent sources that are statistically twisted in the space-frequency and space-time domains. Beginning with the superposition rule for genuine partially coherent sources, we derive source plane expressions for the cross-spectral density (CSD) and mutual coherence functions (MCFs) for twisted space-frequency and space-time Gaussian Schell-model (GSM) beams. Using the Fresnel approximation to the free-space Green’s function, we then paraxially propagate the CSD and MCF to any plane z\u3e 0. We discuss the beams’ behavior as they propagate, with particular emphasis on how the beam shape rotates or tumbles versus z. To validate our analysis, we simulate the generation and subsequent propagation of twisted space-frequency and space-time GSM beams. We compare the simulated moments to the corresponding theoretical predictions and find them to be in excellent agreement. Lastly, we describe how to physically synthesize twisted space-frequency and space-time partially coherent sources. © 2020, The Author(s)

Controlling the Spatial Coherence of an Optical Source Using a Spatial Filter

This paper presents the theory for controlling the spectral degree of coherence via spatial filtering. Starting with a quasi-homogeneous partially coherent source, the cross-spectral density function of the field at the output of the spatial filter is found by applying Fourier and statistical optics theory. The key relation obtained from this analysis is a closed-form expression for the filter function in terms of the desired output spectral degree of coherence. This theory is verified with Monte Carlo wave-optics simulations of spatial coherence control and beam shaping for potential use in free-space optical communications and directed energy applications. The simulated results are found to be in good agreement with the developed theory. The technique presented in this paper will be useful in applications where coherence control is advantageous, e.g., directed energy, free-space optical communications, remote sensing, medicine, and manufacturing