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At least 1,027 records · Page 57

Planetary Defense: Options for Deflection of Near Earth Objects

Several recent near-miss encounters with asteroids and comets have focused attention on the threat of a catastrophic impact with the Earth. This document reviews the historical impact record and current understanding of the number and location of Near Earth Objects (NEO’s) to address their impact probability. Various ongoing projects intended to survey and catalog the NEO population are also reviewed. Details are then given of an MSFC-led study, intended to develop and assess various candidate systems for protection of the Earth against NEO’s. An existing program, used to model the NEO threat, was extensively modified and is presented here. Details of various analytical tools, developed to evaluate the performance of proposed technologies for protection against the NEO threat, are also presented. Trajectory tools, developed to model the outbound path a vehicle would take to intercept or rendezvous with a target asteroid or comet, are described. Also, details are given of a tool that was created to model both the un-deflected inbound path of an NEO as well as the modified, post-deflection, path. The number of possible options available for protection against the NEO threat was too numerous for them to all be addressed within the study; instead, a representative selection were modeled and evaluated. The major output from this work was a novel process by which the relative effectiveness of different threat mitigation concepts can be evaluated during future, more detailed, studies. In addition, several new or modified mathematical models were developed to analyze various proposed protection systems. A summary of the major lessons learned during this study is presented, as are recommendations for future work. It is hoped that this study will serve to raise the level attention about this very real threat and also demonstrate that successful defense is both possible and practicable, provided appropriate steps are taken.

Planets↗

Modeling hepatitis C virus kinetics during liver transplantation highlights the role of the liver in virus clearance

While the liver, specifically hepatocytes, are widely accepted as the main source of hepatitis C virus (HCV) production, the role of the liver/hepatocytes in clearance of circulating HCV remains unknown. Frequent HCV kinetic data were recorded and mathematically modeled from five liver transplant patients throughout the anhepatic (absence of liver) phase and for 4 hr post-reperfusion. During the anhepatic phase, HCV remained at pre-anhepatic levels (n = 3) or declined (n = 2) with t 1/2 ~1 hr. Immediately post-reperfusion, virus declined in a biphasic manner in four patients consisting of a rapid decline (t 1/2 = 5 min) followed by a slower decline (t 1/2 = 67 min). Consistent with the majority of patients in the anhepatic phase, when we monitored HCV clearance at 37°C from culture medium in the absence/presence of chronically infected hepatoma cells that were inhibited from secreting HCV, the HCV t 1/2 in cell culture was longer in the absence of chronically HCV-infected cells. The results suggest that the liver plays a major role in the clearance of circulating HCV and that hepatocytes may be involved.

59 BASIC BIOLOGICAL SCIENCES↗

A model for closing the inviscid form of the average-passage equation system

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

Adamczyk, J. J.↗

A model for closing the inviscid form of the average-passage equation system

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

Adamczyk, J. J.↗

Ergodic Lagrangian dynamics in a superhero universe

We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A maximum principle re-entry study

Mathematical model of maximum principle of Pontryagin used to find point-to-point reentry trajectory of space vehicle

REENTRY TRAJECTORY↗

Modeling suggests SARS-CoV-2 rebound after nirmatrelvir-ritonavir treatment is driven by target cell preservation coupled with incomplete viral clearance

In a subset of SARS-CoV-2-infected individuals treated with the antiviral nirmatrelvir-ritonavir, the virus rebounds following treatment. The mechanisms driving this rebound are not well understood. We used a mathematical model to describe the longitudinal viral load dynamics of 51 individuals treated with nirmatrelvir-ritonavir, 20 of whom rebounded. Target cell preservation, either by a robust innate immune response or initiation of N-R near the time of symptom onset, coupled with incomplete viral clearance, appears to be the main factor leading to viral rebound. Moreover, the occurrence of viral rebound is likely influenced by the time of treatment initiation relative to the progression of the infection, with earlier treatments leading to a higher chance of rebound. A comparison with an untreated cohort suggests that early treatments with nirmatrelvir-ritonavir may be associated with a delay in the onset of an adaptive immune response. Nevertheless, our model demonstrates that extending the course of nirmatrelvir-ritonavir treatment to a 10-day regimen may greatly diminish the chance of rebound in people with mild-to-moderate COVID-19 and who are at high risk of progression to severe disease. Altogether, our results suggest that in some individuals, a standard 5-day course of nirmatrelvir-ritonavir starting around the time of symptom onset may not completely eliminate the virus. Thus, after treatment ends, the virus can rebound if an effective adaptive immune response has not fully developed. These findings on the role of target cell preservation and incomplete viral clearance also offer a possible explanation for viral rebounds following other antiviral treatments for SARS-CoV-2.

60 APPLIED LIFE SCIENCES↗

Parsimonious models of in-host viral dynamics and immune response

Mathematical models of in-host viral dynamics and immune response are a vital tool for patient-specific estimation of the initial viral load, prediction of the course of an infection, etc. The COVID-19 pandemics has given impetus to the development of models with an ever-increasing degree of complexity. We show that one of the most popular models---the Target Cell Limited model---fails the identifiability test, i.e., its parameters cannot be uniquely inferred from readily available data such as viral load measurements. Here, we present a model that is both identifiable and parsimonious according to information criteria. Our model's predictions match both reported observations of COVID-19 patients and predictions of its more complex counterparts.

60 APPLIED LIFE SCIENCES↗

Modal analysis and control of flexible manipulator arms

The possibility of modeling and controlling flexible manipulator arms was examined. A modal approach was used for obtaining the mathematical model and control techniques. The arm model was represented mathematically by a state space description defined in terms of joint angles and mode amplitudes obtained from truncation on the distributed systems, and included the motion of a two link two joint arm. Three basic techniques were used for controlling the system: pole allocation with gains obtained from the rigid system with interjoint feedbacks, Simon-Mitter algorithm for pole allocation, and sensitivity analysis with respect to parameter variations. An improvement in arm bandwidth was obtained. Optimization of some geometric parameters was undertaken to maximize bandwidth for various payload sizes and programmed tasks. The controlled system is examined under constant gains and using the nonlinear model for simulations following a time varying state trajectory.

Neto, O. M.↗

Posiva's Onkalo{sup R} FST (Full-Scale In Situ System Test) - 20051

The FST - Full-scale In Situ System Test - is a unique full-scale demonstration of disposal system in crystalline host rock. The FST was constructed in ONKALO{sup R} demonstration area at the disposal depth of 420 metres, in Posiva's actual final disposal facility at Olkiluoto, Finland. The demonstration has included design, manufacture, installation and comprehensive instrumentation for monitoring the evolution of the disposal system and its components. The demonstration tunnel and experimental deposition holes were excavated in 2010 in ONKALO to address that they can be excavated to meet the requirements set for them. Two experimental deposition holes, bored in the floor of the tunnel, host each a canister surrounded by bentonite clay buffer rings/segments in the holes. Inside the canisters are heating elements to simulate decay heat emitted by spent fuel. The tunnel part used for the test is about 50 m long and it was filled with bentonite clay backfill after the installation of the canisters and buffer components. The tunnel is closed with a steel-reinforced concrete plug. The test is equipped with 500 sensors to monitor early evolution of the system. To forecast the evolution of the system, a mathematical model has been created. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Modeling HIV-1 Within-Host Dynamics After Passive Infusion of the Broadly Neutralizing Antibody VRC01

VRC01 is a broadly neutralizing antibody that targets the CD4 binding site of HIV-1 gp120. Passive administration of VRC01 in humans has assessed the safety and the effect on plasma viremia of this monoclonal antibody (mAb) in a phase 1 clinical trial. After VRC01 infusion, the plasma viral load in most of the participants was reduced but had particular dynamics not observed during antiretroviral therapy. In this paper, we introduce different mathematical models to explain the observed dynamics and fit them to the plasma viral load data. Based on the fitting results we argue that a model containing reversible Ab binding to virions and clearance of virus-VRC01 complexes by a two-step process that includes (1) saturable capture followed by (2) internalization/degradation by phagocytes, best explains the data. This model predicts that VRC01 may enhance the clearance of Ab-virus complexes, explaining the initial viral decay observed immediately after antibody infusion in some participants. Because Ab-virus complexes are assumed to be unable to infect cells, i.e., contain neutralized virus, the model predicts a longer-term viral decay consistent with that observed in the VRC01 treated participants. By assuming a homogeneous viral population sensitive to VRC01, the model provides good fits to all of the participant data. However, the fits are improved by assuming that there were two populations of virus, one more susceptible to antibody-mediated neutralization than the other.

60 APPLIED LIFE SCIENCES↗