A Hypothetical Approach to Cosmic Inflation Incorporating Binary Entropy

The current paper presents an alternative hypothesis for the termination of cosmic inflation based on Huang’s model of spacetime involving the movement of a superfluid through a random resistor network. Using this model, we previously derived a mathematical relationship between the velocity of a reference frame and the probability that a random bond is intact. As an extension of this finding, the permutations of open and closed bonds are now shown to represent potential microstates, thus providing a means of relating motion within the network to binary entropy. Applying this concept to cosmic inflation, termination of this process is an expected consequence of the changes in binary entropy associated with the increasing velocity of expansion.

Twelve Channel ECG Phantom Based on MEGA2560 and DAC-MCP4921

Electrocardiograph (ECG) is one of the diagnostic sciences that is often studied in modern medicine, one of which is to diagnose and treat diseases caused by the heart. Therefore, it is necessary to check the function of the ECG recorder tool, namely by carrying out the tool calibration procedure using Phantom ECG. The purpose of this research is to design a Phantom ECG for a 12 channel ECG device which includes lead I, lead II, lead III, aVR, aVL, aVF, V1, V2, V3, V4, V5, and V6 and completes it with a sensitivity selector. The contribution of this research is that the tool can be used as a calibration tool for the ECG Recorder and can be used as a learning medium in the world of health. In order to create a signal that matches the original, this tool uses a heart signal formation method using a DAC type MCP4921 with an ATMEGA2560 microcontroller and for display settings using a 2.4 inch TFT Nextion Display. The MCP4921 type DAC converts the digital signal data into analog data which will then be forwarded to the resistor network circuit as a signal formation for each lead. In the measurement results, the error in measurements with sensitivity of 0.5 mV, 1.0 mV, and 2.0 mV using an ECG Recorder at BPM 30 is 0.00%, BPM 60 is 0.00%, BPM 120 is 0.00%, and BPM 180 is 0.56%. The results showed that the biggest error was found in BPM 180, which was 0.56%.

Resistor-network formulation of forced convection in asymmetrically-heated channels - hydrodynamically-developed laminar flow

The computation of forced-convective heat transfer from the walls of an asymmetrically heated channel to the fluid passing through in a laminar, hydrodynamically-developed flow is known as the asymmetric Graetz problem. Several analytical and numerical solutions for this problem have been published and many variations and extensions have been investigated. Recently, there has been a renewed interest in this problem due to its applications in emerging areas such as microchannels and fuel cells. In the present work, the asymmetric Graetz problem is examined in a resistor-network framework. The formulation of the problem in terms of three convective resistances leads to temperature-independent Nusselt numbers that are free of the singularities found in previous results. The proposed approach also offers more detail regarding the split of heat transfer between the channel walls and the flow. This work is part of an ongoing project on resistor-network modeling and characterization of multi-temperature convection problems.

Grove Arctic Curves from Periodic Cluster Modular Transformations

Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge probabilities. Using the machinery of asymptotics of multivariate generating functions, this lets us explicitly compute arctic curves, generalizing the arctic circle theorem of Petersen and Speyer. Our class of probability measures is sufficiently general that the limit shapes exhibit all solid and gaseous phases expected from the classification of ergodic Gibbs measures in the resistor network model.