Calculations of The Change of State of a Gas By Integrating The Partial Derivatives

It will not be denied that the calculations of the change of state for a gas is highly important in most engineering applications. For determining the gas’s properties such as the pressure (P), the volume (V) and the temperature (T), engineers and scientists uses the Boyle’s, Charles’s and Gay-Lussac’s (B-C-G) law of P1V1/T1=P2V2/T2. Although the B-C-G law provides the accurate property values of a gas, it give no detailed information embedded in the process when a gas changes its state. In this study, the author theoretically carried out the integrations of the partial differentials when differentiating the B-C-G law, which has not been tried by anyone up to now. The integration results of this study were thoroughly compared with the experimentally measured data and it was confirmed that the integration methods suggested in this study accurately provides the differential properties on ΔP, ΔV and ΔT. In addition to it, through the stepwise analysis of the integration of the partial differentials, it revealed that the efficiency in the change of state of a gas inherently exists higher than the Carnot cycle, which is operating between the same conditions. Therefore, the results of this study can be lead to the conclusion that all changes of state of all materials inevitably accompanies an energy loss and it is a natural phenomenon.

Testing for Wearability and Reliability of TPU Lamination Method in E-Textiles

Electronic textiles (e-textiles) and wearable computing have been emerging increasingly during the last decade. Since the market interest and predictions have grown, the research into increasing reliability and durability of wearables and e-textiles is developing rapidly. The washability of different integration methods and resistance to mechanical stress are the main obstacles being tackled. However, the freedom of movement and overall comfort is still often overlooked during the development phase. It is essential to see the e-textile product as a whole and consider several aspects of user experience. This work will focus on developing and improving the thermoplastic polyurethane (TPU) lamination integration method for e-textiles. In the work, a stretchable copper-polyimide based circuit was laminated onto knit fabric using various TPU films and stacks. The study shares measurable characteristics to determine which material assembly and design would ensure the highest durability for the electronics part without losing its original textile softness, flexibility and stretchability.

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models described in terms of Standard Absolute Coordinates

A classical approach to the MBS modeling is to use absolute coordinates, i.e. a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as alternative approach to the singularity-free time integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. A framework for interfacing Lie group integrators to standard EOM formulations is presented in this paper. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. The direct product group SO(3)xR3; and the semidirect product group SE(3) are use for representing rigid body motions. The key element of this method is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations. This embedding of Lie group integration methods allows for interfacing with standard vector space integration methods.

The Periodicity of the Accuracy of Numerical Integration Methods for the Solution of Different Engineering Problems

Newton-Cotes integration formulae have been researched for a long time, but the topic is still of interest since the correctness of the techniques has not yet been explicitly defined in a sequence for diverse engineering situations. The purpose of this paper is to give the readers an overview of the four numerical integration methods derived from Newton-Cotes formula, namely the Trapezoidal rule, Simpson's 1/3rd rule, Simpson's 3/8th rule, and Weddle's rule, as well as to demonstrate the periodicity of the most accurate methods for solving each engineering integral equation by varying the number of sub-divisions. The exact expressions by solving the numerical integral equations have been determined by Maple program and comparisons have been done using Python version 3.8.

Benchmarking atlas-level data integration in single-cell genomics

Single-cell atlases often include samples that span locations, laboratories and conditions, leading to complex, nested batch effects in data. Thus, joint analysis of atlas datasets requires reliable data integration. To guide integration method choice, we benchmarked 68 method and preprocessing combinations on 85 batches of gene expression, chromatin accessibility and simulation data from 23 publications, altogether representing >1.2 million cells distributed in 13 atlas-level integration tasks. We evaluated methods according to scalability, usability and their ability to remove batch effects while retaining biological variation using 14 evaluation metrics. We show that highly variable gene selection improves the performance of data integration methods, whereas scaling pushes methods to prioritize batch removal over conservation of biological variation. Overall, scANVI, Scanorama, scVI and scGen perform well, particularly on complex integration tasks, while single-cell ATAC-sequencing integration performance is strongly affected by choice of feature space. Our freely available Python module and benchmarking pipeline can identify optimal data integration methods for new data, benchmark new methods and improve method development.

One-Parameter Controlled Non-Dissipative Unconditionally Stable Explicit Structure-Dependent Integration Methods with No Overshoot

Although many families of integration methods have been successfully developed with desired numerical properties, such as second order accuracy, unconditional stability and numerical dissipation, they are generally implicit methods. Thus, an iterative procedure is often involved for each time step in conducting time integration. Many computational efforts will be consumed by implicit methods when compared to explicit methods. In general, the structure-dependent integration methods (SDIMs) are very computationally efficient for solving a general structural dynamic problem. A new family of SDIM is proposed. It exhibits the desired numerical properties of second order accuracy, unconditional stability, explicit formulation and no overshoot. The numerical properties are controlled by a single free parameter. The proposed family method generally has no adverse disadvantage of unusual overshoot in high frequency transient responses that have been found in the currently available implicit integration methods, such as the WBZ-α method, HHT-α method and generalized-α method. Although this family method has unconditional stability for the linear elastic and stiffness softening systems, it becomes conditionally stable for stiffness hardening systems. This can be controlled by a stability amplification factor and its unconditional stability is successfully extended to stiffness hardening systems. The computational efficiency of the proposed method proves that engineers can do the accurate nonlinear analysis very quickly.

Modern methods of direct numerical simulations of transfer processes in random media

The paper considers the methods of direct numerical investigation of the behaviour of dynamical systems of explosive type under the influence of random noise. Dynamical systems are described by a system of nonstationary ordinary differential equations (ODE). The dynamics of the system, taking into account random noise, is described by a system of stochastic ordinary differential equations (SODE). The paper provides an overview of modern algorithms based on modifications of Runge – Kutta integration methods. The features of the analysis of weak and strong convergence of the SODE integration methods are described. Methods for generating random noise with complex temporal structure (color noise) are described. The method of numerical solution of the system of SODE is used to generate random color noise. Examples of the study of the influence of random noise on biological and mechanical systems of explosive type are presented. It is shown that random noises acting on such systems qualitatively change the character of their behaviour.

Analysis of GNSS, Hydroacoustic and Optoelectronic Data Integration Methods Used in Hydrography

The integration of geospatial data in hydrography, performed using different measurement systems, involves combining several study results to provide a comprehensive analysis. Each of the hydroacoustic and optoelectronic systems is characterised by a different spatial reference system and the method for technical implementation of the measurement. Therefore, the integration of hydrographic data requires that problems in selected fields of electronics, geodesy and physics (acoustics and optics) be solved. The aim of this review is to present selected fusion methods applying the data derived from Global Navigation Satellite System (GNSS), Real Time Kinematic (RTK) measurements, hydrographic surveys, a photogrammetric pass using unmanned vehicles and Terrestrial Laser Scanning (TLS) and compare their accuracy. An additional goal is the evalution of data integration methods according to the International Hydrographic Organization (IHO) S-44 standard. The publication is supplemented by implementation examples of the integration of geospatial data in the Geographic Information System (GIS). The methods described indicate the lack of a uniform methodology for data fusion due to differences in both the spatial reference systems and the techniques used. However, the integration of hydroacoustic and optoelectronic data allows for high accuracy geospatial data to be obtained. This is confirmed by the methods cited, in which the accuracy of integrated geospatial data was in the order of several centimetres.

Investigating the optimal integration of airborne, ship-borne, satellite and terrestrial gravity data for use in geoid determination

<p>Each gravity observation technique has different parameters and contributes to different pieces of the gravity spectrum. This means that no one gravity dataset is able to model the Earth’s gravity field completely and the best gravity map is one derived from many sources. Therefore, one of the challenges in gravity field modelling is combining multiple types of heterogeneous gravity datasets. The aim of this study is to determine the optimal method to produce a single gravity map of the Canterbury case study area, for the purposes of use in geoid modelling. This objective is realised through the identification and application of a four-step integration process: purpose, data, combination and assessment. This includes the evaluation of three integration methods: natural neighbour, ordinary kriging and least squares collocation. As geoid modelling requires the combination of gravity datasets collected at various altitudes, it is beneficial to be able to combine the dataset using an integration method which operates in a three-dimensional space. Of the three integration methods assessed, least squares collocation is the only integration method which is able to perform this type of reduction. The resulting product is a Bouguer anomaly map of the Canterbury case study area, which combines satellite altimetry, terrestrial, ship-borne, airborne, and satellite gravimetry using least squares collocation.</p>