Analysis of travelling waves associated with the modelling of aerosolised skin grafts

A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained

How People Judge What Is Reasonable

A classic debate concerns whether reasonableness should be understood statistically (e.g., reasonableness is what is common) or prescriptively (e.g., reasonableness is what is good). This Article elaborates and defends a third possibility. Reasonableness is a partly statistical and partly prescriptive “hybrid,” reflecting both statistical and prescriptive considerations. Experiments reveal that people apply reasonableness as a hybrid concept, and the Article argues that a hybrid account offers the best general theory of reasonableness. First, the Article investigates how ordinary people judge what is reasonable. Reasonableness sits at the core of countless legal standards, yet little work has investigated how ordinary people (i.e., potential jurors) actually make reasonableness judgments. Experiments reveal that judgments of reasonableness are systematically intermediate between judgments of the relevant average and ideal across numerous legal domains. For example, participants’ mean judgment of the legally reasonable number of weeks’ delay before a criminal trial (ten weeks) falls between the judged average (seventeen weeks) and ideal (seven weeks). So too for the reasonable num- ber of days to accept a contract offer, the reasonable rate of attorneys’ fees, the reasonable loan interest rate, and the reasonable annual number of loud events on a football field in a residential neighborhood. Judgment of reasonableness is better predicted by both statistical and prescriptive factors than by either factor alone. This Article uses this experimental discovery to develop a normative view of reasonableness. It elaborates an account of reasonableness as a hybrid standard, arguing that this view offers the best general theory of reasonableness, one that applies correctly across multiple legal domains. Moreover, this hybrid feature is the historical essence of legal reasonableness: the original use of the “reasonable person” and the “man on the Clapham omnibus” aimed to reflect both statistical and prescriptive considerations. Empirically, reasonableness is a hybrid judgment. And normatively, reasonableness should be applied as a hybrid standard

Doctor of Philosophy

dissertationGeometric abnormalities of the human hip joint, as found in femoroacetabular impingement (FAI) and acetabular dysplasia, alter hip biomechanics and may be the primary causes of osteoarthritis in young adults. However, empirical evidence of direct correlations between abnormal geometry, altered biomechanics, and osteoarthritis is scarce. Also, clinical measures used to diagnose FAI and dysplasia still have substantial limitations, including questions about their reliability, assumptions about hip joint geometry and their ability to definitively distinguish pathologic from normal hips. The goals of this dissertation are twofold. First, a set of tools are presented and applied to quantify three-dimensional (3D) anatomical differences between hips with FAI and control subjects. The 3D tools were developed, validated and applied to patients with a subtype of FAI, called cam FAI, to improve basic understanding of the spectrum of FAI deformities, and to provide meaningful new metrics of morphology that are relatable to current diagnostic methods and translate easily for clinical use. The second goal of this dissertation is to improve our understanding of intra-articular hip contact mechanics as well as hip joint kinematics and muscle forces. To do so, a finite element study of intraarticular cartilage contact mechanics was completed with a cohort of live human subjects, using a validated modeling protocol. Finally, musculoskeletal modeling was used with gait data from healthy subjects and acetabular dysplasia patients to provide preliminary estimates of hip joint kinematics, kinetics, and muscle forces and compare differences between the groups. The translational methods of this dissertation utilized techniques from orthopaedics, computer science, physical therapy, mechanics, and medical imaging. Results from this dissertation offer new insight into the complex pathomechanics and pathomorphology of FAI and acetabular dysplasia. Application and extension of the work of this dissertation has the potential to help establish links between FAI and dysplasia with osteoarthritis and to improve patient care

Catastrophic Failure Modes Assessment of the International Space Station Alpha

This report summarizes a series of analyses to quantify the hazardous effects of meteoroid/debris penetration of Space Station Alpha manned module protective structures. These analyses concentrate on determining (a) the critical crack length associated with six manned module pressure wall designs that, if exceeded, would lead to unstopped crack propagation and rupture of manned modules, and (b) the likelihood of crew or station loss following penetration of unsymmetrical di-methyl hydrazine tanks aboard the proposed Russian FGB ('Tug') propulsion module and critical elements aboard the control moment gyro module (SPP-1). Results from these quantified safety analyses are useful in improving specific design areas, thereby reducing the overall likelihood of crew or station loss following orbital debris penetration

Spatial Parameter Identification for MIMO Systems in the Presence of Non-Gaussian Interference

Reliable identification of spatial parameters for multiple-input multiple-output (MIMO) systems, such as the number of transmit antennas (NTA) and the direction of arrival (DOA), is a prerequisite for MIMO signal separation and detection. Most existing parameter estimation methods for MIMO systems only consider a single parameter in Gaussian noise. This paper develops a reliable identification scheme based on generalized multi-antenna time-frequency distribution (GMTFD) for MIMO systems with non-Gaussian interference and Gaussian noise. First, a new generalized correlation matrix is introduced to construct a generalized MTFD matrix. Then, the covariance matrix based on time-frequency distribution (CM-TF) is characterized by using the diagonal entries from the auto-source signal components and the non-diagonal entries from the cross-source signal components in the generalized MTFD matrix. Finally, by making use of the CM-TF, the Gerschgorin disk criterion is modified to estimate NTA, and the multiple signal classification (MUSIC) is exploited to estimate DOA for MIMO system. Simulation results indicate that the proposed scheme based on GMTFD has good robustness to non-Gaussian interference without prior information and that it can achieve high estimation accuracy and resolution at low and medium signal-to-noise ratios (SNRs)

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

An Abductive Argument from Depression and Anxiety to Christian Personal Holiness

The science on pathological depression and anxiety (D&A) describes religion and spirituality\u27s (R/S) insulating and immunizing effects in roughly 72 to 85 percent of all relevant articles. But the descriptivism of science cannot assign any normative value to a theological worldview. Deductive logic favors theism via Leibnizian contingency, Kalām cosmology, objective morality, fine-tuning of the universe, and abstract conceptualism. The information in DNA, the irreducible complexity of intracellular machinery, the improbability of folded proteins, and the support for common modular design over common ancestry establish a design inference for all of life. Unguided naturalistic simulations fail to surmount the complexity barrier of life, diminishing scientific materialism\u27s explanatory power. After philosophical analysis, a cumulative argument using inference to the best explanation (abduction) favors theism over all other worldviews for the complexity of life, the subsequent neurocognitive mechanisms of D&A, and the effects of R/S on D&A. A minimal facts approach establishes Christian theism with positive responses to divine revelation (RDRs) incurring degrees of relative holiness (DRHs). The Christian and non-Christian alike may respond to general revelations in nature and conscience with subsequent DRHs that allow for insulation and immunization against the vicissitudes of life and, therefore, D&A. But the eternal and final solution for D&A is only through a response to the special revelation of the written and living logos with the subsequent imputed holiness of Jesus Christ