Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Geometric Knowledge of Middle School Students in a Reform-based Mathematics Curriculum

National and international studies have found U.S. elementary students to be weak in their understandings and applications of geometric concepts. The University of Chicago School Mathematics Project's (UCMSP) Everyday Mathematics Program is one of the current reform-based elementary curricula incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. In this study, the geometric knowledge of fifth and sixth graders using the UCSMP curriculum is compared to the knowledge of students using more traditional curricula. Because UCSMP students had been in the program since kindergarten, this research attempts to measure the longitudinal effects of such an approach. Along with an overall score, a subset of test items was used to assign each student a van Hiele level for geometric thinking, as well as a reasoning score. On all measures, UCSMP students substantially outperformed their counterparts, and nearly all differences were significant. Aspects of the UCSMP curriculum and the van Hiele model for learning geometry are discussed relative to these results.     

A System for Three-Dimensional Interactive Simulation of Hand Biomechanics

A real-time interactive graphics simulation of the mechanics of the human thumb has been developed. The simulation utilizes a realistic data structure for the bones of the thumb which may be expanded to include the hand and forearm. This is coupled to a model of the kinematics of the joints in a concurrent processing arrangement in which the dynamic graphical transformations for scaling, translation, rotation, perspective, and clipping are all performed on a special-purpose display processor. The model and the control functions are distributed between this processor and a separate general-purpose superminicomputer. The resulting system presents the user with a realistic simulation of the movements of the thumb in normal and impaired states. The user may choose from a menu of options, including an interactive tendon transfer simulation for the current hand being simulated. He may control (interactively and in real time) the view, observation position, skeletal motion, and parameters for use in the model of joint mechanics. This type of computer modeling, utilizing a realistic three-dimensional data structure, models of musculoskeletal kinematics, and interactive programming, shows great potential for bringing mathematical modeling into useful clinical, research, and educational applications.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Feasibility Study of Batteryless Temperature Transponders Using Miniature Microwave Cavity Resonators

Batteryless temperature transponders have been constructed and tested. The design employs a sensing element consisting of a miniature cavity resonator loaded with a ceramic material of high dielectric constant and large temperature coefficient of resonant frequency. This is connected by thin coaxial cable to a small dipole or sector antenna. Prototypes with sensors 3 mm in diameter have been fabricated and can resolve temperature differences of 0.1°C in air. Signals have been obtained from transponders implanted in anesthetized rats, but antenna orientation is a critical and limiting factor that will require further efforts before a system is capable of operating in freely roaming animals.     

Steric effects on nascent vibrational distributions of the HCN product produced in CN radical reactions with ethane, propane and chloroform

Time-resolved IR emission spectroscopy (TRIES) has been used to study infrared emission in the 3400–3100 cm⁻¹ region from HCN molecules produced when CN radicals abstract a hydrogen atom from ethane, propane, and chloroform. From these observations the nascent vibrational distributions of the HCN produced were derived. The nascent vibrational population distributions of the product HCN in all of the reactions are non-statistical and inverted in both the pure CH stretch (00p) and CH stretch—bend (0np) series.     

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.