145 research outputs found

### Lignin dissolution in deep eutectic solvents : a molecular dynamics study

Deep eutectic solvents (DESs) have shown great potential on lignocellulosic biomass pretreatment. Many DESs are capable of extracting lignin from biomass and dissolving hemicellulose while preserving most of cellulose in lignocellulosic biomass. The objective of this thesis is to understand the interaction between DESs and lignin as well as the role of DES constituents, especially hydrogen bond donor (HBD), in such interactions. DESs with choline chloride as a hydrogen bond acceptor (HBA) and polyol/ carboxylic acid as a HBD were studied for their effects on lignin dissolution behavior. The first part of the thesis focuses on the impact of spatial charge assignment on the simulation of a DES. The results indicate that the spatial charge assignment for DES is a key factor in determining the force/interaction energy, which would further change the microscopic arrangement of HBD/HBA. In the second part of this thesis, solvent structure of DESs with choline chloride as a HBA as well as interaction with lignin were studied via molecular dynamics (MD) simulations. Three HBDs, including ethylene glycol, formic acid, and lactic acid as well as two types of lignin models (GG lignin dimer and Adler lignin) were used to gain comprehensive understanding of the local solvent molecular arrangement, the mechanism of lignin dissolution and the dissociation of lignin from cellulose. The common supramolecular complexes in DES were found to show strong correlation with the solvent hydrogen bond network and lignin dissolution. Specially, both functional groups (hydroxyl group vs. carboxyl group) and oxygen atom number in the HBD of a DES determined its hydrogen bond networks and the strength of its interaction with lignin, which in turn largely defined the structural changes of lignin. Also, the chloride anion as well as HBD would preferentially preposition around hydroxyl groups (e.g., [alpha]-OH and [gamma]-OH) located in the lignin linkages. Such preference implies the potential route for bond cleavage in the lignin depolymerization. Molecular interaction between lignin and a DES played a key role in dissociating lignin from cellulose. We found that the carboxylic acid DESs can detach larger part of lignin from cellulose surface, especially on the hydrophobic surface than the polyol DES. The insights gained in this study would advance the understanding of lignin dissolution at an atomistic level and provide guidance for designing effective DESs for biomass pretreatment as well as lignin extraction and valorization toward sustainable and profitable biorefinery.Includes bibliographical references (pages 81-89)

### Existence of Solutions to a Class of Kazdan-Warner Equations on Finite Graphs

Let $G=(V, E)$ be a connected finite graph, $h$ be a positive function on $V$
and $\lambda _{1}(V)$ be the first non-zero eigenvalue of $-\Delta$. For any
given finite measure $\mu$ on $V$, define functionals \begin{eqnarray*}
J_{ \beta }(u)&=&\frac{1}{2}\int_{V}|\nabla u|^{2}d \mu -\beta
\log\int_{V}he^{u}d \mu,
J_{ \alpha ,\beta }(u)&=&\frac{1}{2}\int_{V}\left(|\nabla u|^{2}- \alpha
u^{2}\right) d \mu -\beta \log\int_{V}he^{u}d \mu \end{eqnarray*} on the
functional space ${\bf H}= \left\{ u\in{\bf W}^{1,2}(V) \Bigg| \int_{V}u\!\
d\mu =0 \right\}.$
For any $\beta \in \mathbb{R}$, we show that $J_{ \beta }(u)$ has a minimizer
$u\in{\bf H}$, and then, based on variational principle, the Kazdan-Warner
equation $\Delta u=-\frac{\beta he^{u}}{\displaystyle{\int_{V}he^{u}d \mu
}}+\frac{\beta }{\text{Vol}(V)}$ has a solution in ${\bf H}$.
If $\alpha < \lambda _{1}(V)$, then for any $\beta \in \mathbb{R} , J_{
\alpha ,\beta }(u)$ has a minimizer in ${\bf H}$, thus the Kazdan-Warner
equation $\Delta u+\alpha\!\ u=-\frac{\beta
he^{u}}{\displaystyle{\int_{V}he^{u}d \mu }}+\frac{\beta }{\text{Vol}(V)}$
has a solution in ${\bf H}$. If $\alpha > \lambda _{1}(V)$, then for any $\beta
\in \mathbb{R}$, $\displaystyle{\inf_{u\in{\bf H}} J_{ \alpha ,\beta }(u) =-
\infty}$. When $\alpha=\lambda_{1}(V)$, the situation becomes complicated: if
$\beta=0$, the corresponding equation is $-\Delta u=\lambda_{1}(V)u$ which has
a solution in ${\bf H}$ obviously; if $\beta>0$, then $\displaystyle{\inf_{u\in
{\bf H}} J_{\alpha,\beta }(u) =- \infty}$; if $\beta<0$, $J_{ \alpha ,\beta
}(u)$ has a minimizer in some subspace of ${\bf H}$.
Moreover, we consider the same problem where higher eigenvalues are involved

### Morphology And Mechanics Of Cortical Folding Associated With Auditory Deprivation

Hearing loss is increasingly becoming a common disabling condition that affects the global population. Functional and structural changes occur in the developing auditory cortex after the onset of auditory deprivation. This study aims at measuring and modeling these changes, which can help understand the pathology of hearing loss and support research on treatment. Specifically, it describes a pipeline of automatically extracting inner and outer cortical surfaces from MRI images and measuring morphological metrics. Then, a two-component finite element mechanical model mimicking gray matter and white matter is used to investigate the causes of measured structural differences between cats with normal hearing and hearing loss. Mechanical parameters, such as shear and bulk modulus, are varied with a view to studying their influence on cortical folding patterns. Compared to hearing cats, cats with hearing loss have decreased cortical curvature and folding index, and increased thickness. By varying the shear modulus and bulk modulus of the gray and white matter at different locations, the mechanical model reveals distinct stable folding patterns. Specific combinations of parameters and locations lead to changes in curvature, folding index, and thickness. The methods used in this study can also be extended to examine cortical morphological characteristics associated with other abnormalities in the developing brain

### GeodesicEmbedding (GE): a high-dimensional embedding approach for fast geodesic distance queries

In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in the original manifold surface. However, directly solving the high-dimensional embedding problem is not feasible due to the large number of variables and the fact that the embedding problem is highly nonlinear. We overcome the challenges with two novel ideas. First, instead of taking all vertices as variables, we embed only the saddle vertices, which greatly reduces the problem complexity. We then compute a local embedding for each non-saddle vertex. Second, to reduce the large approximation error resulting from the purely Euclidean embedding, we propose a cascaded optimization approach that repeatedly introduces additional embedding coordinates with a non-Euclidean function to reduce the approximation residual. Using the precomputation data, our approach can determine the geodesic distance between any two vertices in near-constant time. Computational testing results show that our method is more desirable than previous geodesic distance queries methods

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