Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics

We quantify the numerical error and modeling error associated with replacing a nonlinear nonlocal bond-based peridynamic model with a local elasticity model or a linearized peridynamics model away from the fracture set. The nonlocal model treated here is characterized by a double well potential and is a smooth version of the peridynamic model introduced in n Silling (J Mech Phys Solids 48(1), 2000). The solutions of nonlinear peridynamics are shown to converge to the solution of linear elastodynamics at a rate linear with respect to the length scale $\epsilon$ of non local interaction. This rate also holds for the convergence of solutions of the linearized peridynamic model to the solution of the local elastodynamic model. For local linear Lagrange interpolation the consistency error for the numerical approximation is found to depend on the ratio between mesh size $h$ and $\epsilon$. More generally for local Lagrange interpolation of order $p\geq 1$ the consistency error is of order $h^p/\epsilon$. A new stability theory for the time discretization is provided and an explicit generalization of the CFL condition on the time step and its relation to mesh size $h$ is given. Numerical simulations are provided illustrating the consistency error associated with the convergence of nonlinear and linearized peridynamics to linear elastodynamics

Numerical convergence of finite difference approximations for state based peridynamic fracture models

In this work, we study the finite difference approximation for a class of nonlocal fracture models. The nonlocal model is initially elastic but beyond a critical strain the material softens with increasing strain. This model is formulated as a state-based perydynamic model using two potentials: one associated with hydrostatic strain and the other associated with tensile strain. We show that the dynamic evolution is well-posed in the space of H\"older continuous functions $C^{0,\gamma}$ with H\"older exponent $\gamma \in (0,1]$. Here the length scale of nonlocality is $\epsilon$, the size of time step is $\Delta t$ and the mesh size is $h$. The finite difference approximations are seen to converge to the H\"older solution at the rate $C_t \Delta t + C_s h^\gamma/\epsilon^2$ where the constants $C_t$ and $C_s$ are independent of the discretization. The semi-discrete approximations are found to be stable with time. We present numerical simulations for crack propagation that computationally verify the theoretically predicted convergence rate. We also present numerical simulations for crack propagation in precracked samples subject to a bending load.Comment: 42 pages, 11 figure

Digital Photo Frame

With the advancement in semiconductor technology, scope for development of embedded systems has increased manifolds. New processors with improved computing capabilities and low power consumption have further accelerated the developments in embedded domain. Consumers are looking for affordable multimedia devices with high performance and durability making embedded developers to think creatively and use all resources at hand to meet the desired user specifications. This is one such attempt by designing a digital photo frame with 5 inch LCD display intended to display high quality BMP images. Small Size and low cost of development can prove to be very useful in the success of the device as a day to day consumer electronics product. Powerful computing capabilities of ARM processor when duly utilised can produce very elegant results

INVESTIGATING CRIME PATTERNS IN A FREIGHT-CENTRIC NEIGHBORHOOD

The flow of freight is integral for the economic development of a country, but with the increase in freight volume, there is an increase in freight externalities as well. There are a few research studying the impact of freight on various environmental and health factors but research on the impact of freight on crime is lacking. The focus of this research is to determine the correlation between freight sources and crime patterns in a freight-centric neighborhood. Occurrences of crime incidents are identified as random, or a part of a pattern or cluster. The effect of freight sources on crime patterns is analyzed via correlation tests, ordinary least square regression, analysis of variance, analysis of covariance, hierarchical nearest neighbor clustering, and Getis-Ord Gi* hotspot analysis. The findings of this research indicate a significant correlation between the presence of warehouses and various types of crimes. Areas with higher freight sources tend to have higher crime densities. The results show a need to understand the interaction of crime patterns with the number of freight sources present to make well-informed decisions on community development, land value, policy making, and crime prevention strategies. Keywords: Livability, freight-centric neighborhood, crime densit

Biology and Ecology of Palmer Amaranth (Amaranthus palmeri)

Palmer amaranth (Amaranthus palmeri S. Wats.) is a troublesome weed of crops in southeastern United States. This research highlights studies on the biology and ecology of Palmer amaranth. Following dispersal in fall, Palmer amaranth seeds require high mean temperatures of 25 to 40 C for germination, which is not likely to occur in South Carolina until the following spring. With dormancy reduction over winter, seeds can germinate at high temperatures (≥25 C) and thermal amplitudes of 15 C during late spring (May) in the presence of light. A majority (\u3e90%) of the non-dormant population in the soil seedbank emerge from early May through mid-July, with two to three peak emergence periods which often follow rainfall events. No difference in emergence was observed between no-tillage and shallow spring tillage situations. Early canopy closure in drill-seeded soybean (18-cm row width) had a suppressive effect on the emergence of Palmer amaranth cohorts following early July. This is attributed to the decrease in photosynthetic active radiation (PAR) and red:far-red (R:FR) ratio experienced by seeds lying on the soil surface beneath the canopy in no-tillage systems. Seed germination during fall (August to November) is phytochrome-regulated, with germination stimulation by R light and inhibition by FR light. Burial of seeds to a 10-cm depth for 3 to 6 months induced dormancy with a R or natural light requirement for germination. Palmer amaranth seeds developing under shade conditions (87% reduction in PAR) showed increased dormancy, a survival mechanism in low-light environment. In addition, seeds maturing in the bottom-third of a mother plant exhibited increased dormancy, partially explaining variability in timing and extent of germination within a single seed population. Besides exhibiting increased seed dormancy, Palmer amaranth showed photosynthetic and morphological acclimation to 87% shading. These characteristics make Palmer amaranth a troublesome weed in crop-production systems. Based on this research, an early-season glyphosate application preferably at the V3 stage of glyphosate-resistant soybean in conjunction with early planting dates (April) with narrow row (18-cm wide) spacing can be a promising strategy to reduce Palmer amaranth interference and seed production and improve soybean yields

Temperature Gradient Effect on Solid-Liqid Interface Properties of Al-Cu Alloy: A Molecular Dynamics Study

Aluminum-copper (Al-Cu) alloys are widely used in the aerospace industry due to their favorable strength-to-weight ratio, good fatigue resistance, and corrosion resistance. These properties make Al-Cu alloys an excellent choice for aircraft structural components that require high strength and low weight. Additive manufacturing (AM), also known as 3D printing, has emerged as a promising processing method for Al-Cu alloys in aerospace manufacturing. AM enables the production of lightweight optimized geometries difficult to manufacture through conventional subtractive methods. AM also reduces material waste by only depositing material where needed in the part geometry. The rapid solidification conditions in AM processes motivate further study of solid-liquid interface properties in Al-Cu alloys. This work examines the solid-liquid interface using molecular dynamics (MD) simulations and the capillary fluctuation method (CFM). CFM facilitates quantitatively determining key interfacial characteristics like stiffness, energy, and anisotropy. Simulations were performed under both equilibrium conditions and applied thermal gradients to replicate AM processes. Applying a thermal gradient across the interface led to an augmentation in stiffness and interfacial free energy while preserving the constancy of anisotropic characteristics. This phenomenon was theoretically elucidated by employing a Taylor expansion of the interfacial free energy function. The equations representing the relationships are: for energy and for stiffness, where G represents the thermal gradient. The present study involved simulations on Al-Cu alloys containing varying concentrations of copper, specifically 2%, 3.58%, and 5.065% Cu. These simulations were conducted at different temperatures, 905K, 888K, and 874K, respectively. A total of eight unique interface orientations were investigated. The obtained results were consistent with the proposed theoretical relationships, thereby confirming the presence of anisotropy independent of the gradient and the validity of the first-order Taylor expansion. This study provides fundamental insights into interfacial phenomena during Al-Cu alloy solidification, which can help optimize AM processes by reducing defects. The calculated parameters have significant implications for larger scale computational models of AM by improving accuracy compared to experiments when incorporating non-equilibrium conditions

2020 Summary of Herbicide Evaluations for Marestail (Horseweed) Control in Soybean

Marestail is one of the most widespread and troublesome weeds in Iowa croplands. It can grow to a height of 1.5 to 6 feet, produce up to 200,000 seeds, and can reduce soybean yields up to 80% if not controlled (Figure 1). Marestail seeds are light and disperse across landscapes with winds. Seeds have little dormancy and can germinate soon after seed shed. In general, 75% of seedlings germinate in fall, remain in rosette-stage until spring, begin stem elongation in April, and start flowering in July. About 25% of seeds germinate in the spring. Due to these unique biological characteristics and a prolonged emergence period, a comprehensive management program is necessary for marestail control