The Chesterfield Pike Plan: A Community Revitalization Plan for Historic Route 1

The Chesterfield Pike Plan complements Chesterfield County’s ongoing efforts to revitalize the northern section of the Jefferson Davis Highway corridor. By focusing on housing and local economic challenges on what is locally known as “The Pike,” this plan explores community revitalization strategies in a diverse inner-ring suburb. The Pike has been impacted by the nationwide trends of suburban poverty and immigrant suburbanization, which present challenges and opportunities in the pursuit of revitalization. Striking a balance between meeting community needs and economic growth requires a plan that identifies ways in which both new private investment and the existing community can benefit. The Chesterfield Pike Plan responds to this need with specific policy and program recommendations that find that balance. Exploring the market affordable housing and community-defining business types along the Pike, this plan identifies multiple ways in which the County can develop each type to strengthen existing residential options while also creating an economic environment to support new business and residential growth. The Chesterfield Pike Plan recommends seven major goals that would support a revitalized Pike for all: 1. Establishment of a countywide, dedicated source of funding for affordable housing 2. Preservation and enhancement of at-risk market affordable housing on the Pike 3. Promotion of the county as an immigrant-friendly place 4. Development of a multicultural public market on the Pike 5. Improvement of existing commercial business conditions on the Pike 6. Promotion of challenge-conscious workforce development on the Pike 7. Expansion and focus of public investment on the Pik

Stochastic TDHF in an exactly solvable model

We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $\Omega$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $\Omega$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.Comment: 23 pages, 8 figures, accepted in Annals of Physic

Cumulative constraint interaction and the equalizer of OT and HG

We show that, in general, Optimality Theory (OT) grammars containing a restricted family of locally-conjoined constraints (Smolensky 2006) make the same typological predictions as corresponding Harmonic Grammar (HG) grammars. We provide an intuition for the generalization using a simple constrast and neutralization typology, as well as a formal proof. This demonstration adds structure to claims about the (non)equivalence of HG and OT with local conjunction (Legendre et al. 2006, Pater 2016) and provides a tool for understanding how different sets of constraints lead to the same typological predictions in HG and OT

Questioning to Resolve Transduction Problems

Elgot & Mezei (1965) show that non-deterministic regular functions (NDRFs) are compositions ρ ⚬ λ of two contradirectional subsequential functions (SSQs), where λ is unbounded lookahead for ρ. Such decompositions facilitate the identification of processes that require supra-SSQ expressivity. We use concepts adapted from decision theory to outline a set of necessary and sufficient properties for a composition ρ ⚬ λ to define a non-SSQ NDRF . These conditions define a set of functions between the IF-WDRFs (McCollum et al. 2018, Hao & Andersson 2019) and proper NDRFs, organized in terms of a precise notion of the degree of lookahead that λ provides for ρ

Generalized multiscale finite element method for a strain-limiting nonlinear elasticity model

In this paper, we consider multiscale methods for nonlinear elasticity. In particular, we investigate the Generalized Multiscale Finite Element Method (GMsFEM) for a strain-limiting elasticity problem. Being a special case of the naturally implicit constitutive theory of nonlinear elasticity, strain-limiting relation has presented an interesting class of material bodies, for which strains remain bounded (even infinitesimal) while stresses can become arbitrarily large. The nonlinearity and material heterogeneities can create multiscale features in the solution, and multiscale methods are therefore necessary. To handle the resulting nonlinear monotone quasilinear elliptic equation, we use linearization based on the Picard iteration. We consider two types of basis functions, offline and online basis functions, following the general framework of GMsFEM. The offline basis functions depend nonlinearly on the solution. Thus, we design an indicator function and we will recompute the offline basis functions when the indicator function predicts that the material property has significant change during the iterations. On the other hand, we will use the residual based online basis functions to reduce the error substantially when updating basis functions is necessary. Our numerical results show that the above combination of offline and online basis functions is able to give accurate solutions with only a few basis functions per each coarse region and updating basis functions in selected iterations.Comment: 19 pages, 2 figures, submitted to Journal of Computational and Applied Mathematic

Phonological opacity as local optimization in Gradient Symbolic Computation

We present a novel approach to counterbleeding rule interactions in Yokuts (Californian) using Gradient Symbolic Computation (GSC). GSC, a dynamical systems model, optimizes two constraint sets: a set specifying a Harmonic Grammar (HG) and a set of quantization constraints preferring discrete symbolic states. During optimization, quantization strength gradually increases, increasing the relative harmony of discrete symbolic vs. intermediate blend states. The output of the system therefore reflects the dynamics of optimization, not simply grammatical harmony. With appropriate dynamics, relatively high harmony intermediate states can trap optimization near less globally harmonic but locally optimal symbolic candidates; this can model Yokuts counterbleeding

Constraint energy minimizing generalized multiscale finite element method for nonlinear poroelasticity and elasticity

In this paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to first solving a nonlinear poroelasticity problem. The arising system consists of a nonlinear pressure equation and a nonlinear stress equation in strain-limiting setting, where strains keep bounded while stresses can grow arbitrarily large. After time discretization of the system, to tackle the nonlinearity, we linearize the resulting equations by Picard iteration. To handle the linearized equations, we employ the CEM-GMsFEM and obtain appropriate offline multiscale basis functions for the pressure and the displacement. More specifically, first, auxiliary multiscale basis functions are generated by solving local spectral problems, via the GMsFEM. Then, multiscale spaces are constructed in oversampled regions, by solving a constraint energy minimizing (CEM) problem. After that, this strategy (with the CEM-GMsFEM) is also applied to a static case of the above nonlinear poroelasticity problem, that is, elasticity problem, where the residual based online multiscale basis functions are generated by an adaptive enrichment procedure, to further reduce the error. Convergence of the two cases is demonstrated by several numerical simulations, which give accurate solutions, with converging coarse-mesh sizes as well as few basis functions (degrees of freedom) and oversampling layers.Comment: 32 pages, 7 figures, 6 tables, submitted to Journal of Computational Physic

Shacklefords Commercial Development Analysis

King and Queen County believes that economic development is crucial to ensuring a stable economy and high quality of life for residents of the county. With an out-commuting rate of 71% for the entire Middle Peninsula region, residents and businesses are spending their money outside of the region due to a lack of job opportunities and commercial development. However, the intersection of Route 33 and The Trail at Shacklefords within King and Queen County provides a major economic development opportunity for King and Queen County and the Middle Peninsula region. Through a one-semester research project, students in a VCU Commercial Revitalization course were invited by King and Queen County Administrator, Thomas Swartzwelder, to complete research on King and Queen County’s opportunity to attract the commuting traffic passing Shacklefords each day, as well as meet the desires of the community and the existing plans for this site. A VDOT Smart Scale funded development, currently in the design phase, will create a telecommuting center at the Shacklefords site, and relocate the offices of the Middle Peninsula Planning District Commission (PDC) to the same development. On a separate site at the same intersection, a privately established craft brewery site represents a convergence of new development that could spur additional commercial opportunities