Jacob Woods

Jacob Woods

he/him

I am a Phd student in Mathematics at Temple University my research interests are in the field of Applied Mathematics, I am especially interested in questions related to biology and ecology. I primarily use ODE, PDE and agent-based modeling techniques, implementing them with custom-coded numerical methods to simulate models incorporating data.

Posts by Collection

portfolio

publications

talks

Bridging the Gap Between 1D Car-Following and 2D Swarming

Published:

Multi-agent systems in multiple dimensions occur in many contexts like human traffic, flocks of birds, and schools of fish. These systems can produce complex emergent phenomena which are not immediately apparent from the individual agents’ law of motion and objectives. In many cases, the emergent behaviors are beneficial like: protection from predators, greater social interactions, and more efficient movement in the environment. One-dimensional traffic flow also exhibits emergent structures; but these are frequently undesirable, like phantom jams and traffic waves. In this talk we present ideas for models that draw from both traffic models and swarming models to produce new models for multi-agent dynamics in 2D and 3D that exhibit agent-following behavior like cars and thus can develop dynamic instabilities. These models may describe swarming with leader effects and driving in the absence of roadways, more accurately than classical swarming models. We showcase via simulations and some analytical results, how the new models can produce very different emergent swarm behavior than existing swarming models.

Mathematical Models for the Spread of Spotted Lanternfly Across Multiple Scales

Published:

In 2014 the spotted lanternfly was introduced to Pennsylvania and with its ability to severely compromise lumber, grape and crop production has become a species of great concern. We present principled models for the spread of the species, capturing their hopping behavior across hosts, as observed and documented in the field. A calibrated model prototype is showcased with vineyards in mind, capturing how spotted lanternflies move between hosts in landscapes with different host geometries over the course of a season. We demonstrate how different geometries of hosts like those found in vineyards, deep forest, or edge ecosystems produce different emergent patterns of spread. We also connect the small-scale hopping model to large-scale models which forecast the spread over areas the size of the entire Northeastern US or of California.

Mathematical Framework for Modeling the Movement of Adult Spotted Lanternfly into Vineyards and Application for Optimal Control

Published:

The spotted lanternfly (Lycorma delicatula, SLF) is a plant hopper that primarily feeds on hosts such as the tree of heaven and grape vines. Hosts may succumb and die from the infestation, posing a significant concern for the agricultural industry; in particular, vineyards are at great risk. SLF can damage and even kill vines throughout a season. This, coupled with the emergence of adults—the time when SLF are most mobile—coinciding with grape harvest, makes the control of SLF very challenging in these landscapes.

Modeling the Spread of Spotted Lanternfly in Vineyards and Across Multiple Scales

Published:

In 2014 the spotted lanternfly was introduced to Pennsylvania and with its ability to severely compromise lumber, grape and crop production has become a species of great concern. We present principled models for the spread of the species, capturing their hopping behavior across hosts, as observed and documented in the field. A calibrated model prototype is showcased with vineyards in mind, capturing how spotted lanternflys move between hosts in landscapes with different host geometries over the course of a season. We demonstrate the implications of this model on existing vineyards using data for host locations in and around real vineyards. We also connect the small-scale hopping model to large-scale models which forecast the spread over areas the size of the entire Northeastern US or of California.

Optimal Routing of Multi-Agent Swarms Via Low-Dimensional Approximation

Published:

Swarming models can demonstrate patterns similar to those seen in schools of fish or flocks of birds, human crowds, and swarms of robots moving together. Here we assume agents in the swarm know about the locations and velocities of nearby agents but may not have a complete picture of the geometry and dynamics of the swarm as a whole. A key question we investigate is how can one navigate the swarm through a landscape with obstacles. We present a method for approximating a swarm of agents macroscopically and navigating this macroscopic swarm through a landscape using optimal control. Then we present how one may add dynamics to the microscopic swarming model to allow the swarm to follow the computed path well attempting to minimize the deformation done to the swarm at a large scale.

Agent-Based Modeling of Collective Foraging and Movement in Bison Herds

Published:

Bison are an important species in the habitats they occupy, providing services to the ecosystem through their collective grazing and movement, while having significant cultural importance for Indigenous food sovereignty. In the late 19th century, they were brought to the brink of extinction due to hunting but through significant conservation efforts, bison have been reintroduced to the American grasslands, and efforts have been made to help facilitate the services they provide to the ecosystem. It is unknown what foraging strategies bison use in a landscape and it isn’t clear what dictates changes in the bison’s behavioral states, such as grazing, resting, and moving. In this talk, I present a model inspired by the bison’s behavior that captures how the bison move through a landscape and their social interactions. This model is calibrated with GPS movement data and informed in collaboration with expert ecologists’ insights, allowing exploration of scenarios such as enclosure design and herd expansions. This work demonstrates how mathematical models of collective behavior can provide both theoretical insight and practical tools for conservation and ecosystem management.

teaching

Numerical Analysis Lab

Lab Instructor, Temple University, Mathematics, 2021

Ran a lab for undergraduates to review course material and implement numerical methods in MATLAB under my supervison with demonstrations of some numerical methods.

Calculus I

Undergraduate Instructor, Temple University, Mathematics, 2022

Taught sections of Calculus I in Spring 2022 and Summer 2022/2025.

Numerical Analysis Graduate Summer Review Session

Graduate Review Session Instructor, Temple University, Mathematics, 2023

Taught a summer review course for graduate students to review the material learned in their introductory numerical analysis course to prepare them for their qualifying exams.

Review Session: Precalculus

Undergraduate Review Session Leader, Temple University, Mathematics, 2024

Hosted Review Sessions for students in Precalculus.