Search results for: zero point energy

Authors: D. S. Palimkar

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Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Pakkinee Chitsakul

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In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: cut locus, flat torus, geodesics

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Authors: P. Valdez, M. Pelissero, A. Haim, F. Muiño, F. Galia, R. Tula

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As a result of the studies performed on the wave energy resource worldwide, a research project was set up to harvest wave energy for its conversion into electrical energy. Within this framework, a theoretical model of the electromechanical energy harvesting system, developed with MATLAB’s Simulink software, will be provided. This tool recreates the site conditions where the device will be installed and offers valuable information about the amount of energy that can be harnessed. This research provides a deeper understanding of the utilization of wave energy in order to improve the efficiency of a 1:1 scale prototype of the device.

Keywords: electromechanical device, modeling, renewable energy, sea wave energy, simulation

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Authors: Ahmed Al-Adaileh, Souheil Khaddaj

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Outcomes of exhaustion of natural resources started influencing each spirit on this planet. Energy is an essential factor in this aspect. To restore the circumstance to the appropriate track, all attempts must focus on two fundamental branches: producing electricity from clean and renewable reserves and decreasing the overall unnecessary consumption of energy. The focal point of this paper will be on lessening the power consumption in the household's segment. This paper is an attempt to give a clear understanding of a framework called Reduction of Energy Consumption in Household Sector (RECHS) and how it should help householders to reduce their power consumption by substituting their household appliances, turning-off the appliances when stand-by modus is detected, and scheduling their appliances operation periods. Technically, the framework depends on utilizing Z-Wave compatible plug-ins which will be connected to the usual house devices to gauge and control them remotely and semi-automatically. The suggested framework underpins numerous quality characteristics, for example, integrability, scalability, security and adaptability.

Keywords: smart energy management systems, internet of things, wireless mesh networks, microservices, cloud computing, big data

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Authors: Andrés Gomez-Casseres, Rubén Contreras

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In this paper, a bidirectional boost converter operated in Discontinuous Conduction Mode (DCM) is presented as a suitable power conditioning circuit for tuning of kinetic energy harvesters without the need of a battery. A nonlinear control scheme, composed by two linear controllers, is used to control the average value of the input current, enabling the synthesization of complex loads. The converter, along with the control system, is validated through SPICE simulations using the LTspice tool. The converter model and the controller transfer functions are derived. From the simulation results, it was found that the input current distortion increases with the introduced phase shift and that, such distortion, is almost entirely present at the zero-crossing point of the input voltage.

Keywords: average current control, boost converter, electrical tuning, energy harvesting

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Authors: Akhila Konala, Jagadeeswara Reddy Vennapusa, Sujay Chattopadhyay

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The energy consumption of humankind is growing day by day due to an increase in the population, industrialization and their needs for living. Fossil fuels are the major source of energy to satisfy energy needs, which are non-renewable energy resources. So, there is a need to develop green resources for energy production and storage. Phase change materials (PCMs) derived from plants (green resources) are well known for their capacity to store the thermal energy as latent heat during their phase change from solid to liquid. This property of PCM could be used for storage of thermal energy. In this study, a composite with fatty acid (caprylic acid; M.P 15°C, Enthalpy 179kJ/kg) as a phase change material and expanded perlite as support porous matrix was prepared through direct impregnation method for thermal energy storage applications. The prepared composite was characterized using Differential scanning calorimetry (DSC), Field Emission Scanning Electron Microscope (FESEM), Thermal Gravimetric Analysis (TGA), and Fourier Transform Infrared (FTIR) spectrometer. The melting point of the prepared composite was 15.65°C, and the melting enthalpy was 82kJ/kg. The surface nature of the perlite was observed through FESEM. It was observed that there are micro size pores in the perlite surface, which were responsible for the absorption of PCM into perlite. In TGA thermogram, the PCM loss from composite was started at ~90°C. FTIR curves proved there was no chemical interaction between the perlite and caprylic acid. So, the PCM composite prepared in this work could be effective to use in temperature maintenance of buildings.

Keywords: caprylic acid, composite, phase change materials, PCM, perlite, thermal energy

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Authors: Hussain Ali Bekhet, Nor Hamisham Harun

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The main objective of this paper is to give a comprehensive review of non-renewable energy and renewable energy utilization in Malaysia, including hydropower, solar photovoltaic, biomass and biogas technologies. Malaysia mainly depends on non-renewable energy (natural gas, coal and crude oil) for electricity generation. Therefore, this paper provides a comprehensive review of the energy sector and discusses diversification of electricity generation as a strategy for providing sustainable energy in Malaysia. Energy policies and strategies to protect the non-renewable energy utilization also are highlighted, focusing in the different sources of energy available for high and sustained economic growth. Emphasis is also placed on a discussion of the role of renewable energy as an alternative source for the increase of electricity supply security. It is now evident that to achieve sustainable development through renewable energy, energy policies and strategies have to be well designed and supported by the government, industries (firms), and individual or community participation. The hope is to create a positive impact on sustainable development through renewable sources for current and future generations.

Keywords: Malaysia, non-renewable energy, renewable energy, sustainable energy

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Authors: Cyril Agochi Okorowo

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More than ever human activity relating to uncontrolled greenhouse gas (GHG) and its effects on the earth is gaining greater attention in the global academic and policy discussions. Activities of man have greatly influenced climate change over the years as a result of a consistent increase in the use of fossil fuel energy. Scientists and researchers globally are making significant and devoted efforts towards the development and implementation of renewable energy technologies that are harmless to the environment. One of such energy is solar energy with its source from the sun. There are currently two primary ways of harvesting this energy from the sun: through photovoltaic (PV) panels and through thermal collectors. This work discusses solar energy as the abundant renewable energy in the tropical Nigeria, processes of harvesting the energy and recommends solar energy as an alternative means of electric power generation in a time the demand for power in Nigeria supersedes supply.

Keywords: analysis, energy, design, solar

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Authors: Vicx Farm

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This paper examines the critical role of energy efficiency management and renewable energy in fostering sustainable agricultural practices in Nigeria. With the growing concerns over energy security, environmental degradation, and climate change, there is an urgent need to transition towards more sustainable energy sources and practices in the agricultural sector. Nigeria, being a significant player in the global agricultural market, stands to benefit immensely from integrating energy efficiency measures and renewable energy solutions into its agricultural activities. This paper discusses the current energy challenges facing Nigerian agriculture, explores the potential benefits of energy efficiency and renewable energy adoption, and proposes strategies for effective implementation. The paper concludes with recommendations for policymakers, stakeholders, and practitioners to accelerate the adoption of energy-efficient and renewable energy technologies in Nigerian agriculture, thereby promoting sustainable development and resilience in the sector.

Keywords: energy, agriculture, sustainability, power

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Authors: Marwa Ahmed Abd El Hamied

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In this paper In this paper, a new technique based on Artificial Immunity System (AIS) technique has been developed to track Maximum Power Point (MPP). AIS system is implemented in a photovoltaic system that is subjected to variable temperature and insulation condition. The proposed novel is simulated using Mat Lab program. The results of simulation have been compared to those who are generated from Observation Controller. The proposed model shows promising results as it provide better accuracy comparing to classical model.

Keywords: component, artificial immunity technique, solar energy, perturbation and observation, power based methods

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Authors: Rameshaiah Gowdara Narayanappa, Manikonda Prithvi, Manoj Kumar, Suraj Bhavani, Vikram Singh

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Long ago heating of food was only related to fire or electricity. Heating and storage of consumer foods were satisfied by the use of vacuum thermo flaks, electric heating cans and DC powered heating cans. But many of which did not sustain the heat for a long period of time and were impractical for remote areas. The use of chemical energy for heating foods directed us to think about the applications of exothermic reactions as a source of heat. Initial studies of calcium oxide showed desirability but not feasible because the reaction was uncontrollable and irreversible. In this research work we viewed at crystallization of super saturated sodium acetate trihydrate solution. Supersaturated sodium acetate trihydrate has a freezing point of 540 C (1300 F), but it observed to be stable as a liquid at much lower temperatures. Mechanical work is performed to create an active chemical energy zone within the working fluid, when crystallization process is initiated. Due to this the temperature rises to its freezing point which in turn heats the contents in the storage container. Present work endeavor to design a self-heating storage container is suitable for consumer dedications.

Keywords: crystallization, exothermic reactions, self-heating container, super saturation, vacuum thermo flask

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Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

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Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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Authors: Li Zhu, Binghua Wang, Yong Sun

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China is experiencing the rural development process, with the agritourism complex becoming one of the significant modes. Therefore, it is imperative to understand the energy performance of agritourism complex. This study focuses on a typical case of the agritourism complex and simulates the energy consumption performance on condition of the regular energy system. It was found that HVAC took 90% of the whole energy demand range. In order to optimize the energy supply structure, the hierarchical analysis was carried out on the level of architecture with three main factors such as construction situation, building types and energy demand types. Finally, the energy planning suggestion of the agritourism complex was put forward and the relevant results were obtained.

Keywords: agritourism complex, energy planning, energy demand simulation, hierarchical structure model

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Authors: Amirhossein Khazali, Mohsen Kalantar

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Energy storage units can play an important role to provide an economic and secure operation of future energy systems. In this paper, a stochastic energy and reserve market clearing scheme is presented considering storage energy units. The approach is proposed to deal with stochastic and non-dispatchable renewable sources with a high level of penetration in the energy system. A two stage stochastic programming scheme is formulated where in the first stage the energy market is cleared according to the forecasted amount of wind generation and demands and in the second stage the real time market is solved according to the assumed scenarios.

Keywords: energy and reserve market, energy storage device, stochastic programming, wind generation

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Authors: Richard Lewis

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The following assumptions of the Big Bang theory are challenged and found to be false: the cosmological principle, the assumption that all matter formed at the same time and the assumption regarding the cause of the cosmic microwave background radiation. The evolution of the universe is described based on the conclusion that the universe is finite with a space boundary. This conclusion is reached by ruling out the possibility of an infinite universe or a universe which is finite with no boundary. In a finite universe, the centre of the universe can be located with reference to our home galaxy (The Milky Way) using the speed relative to the Cosmic Microwave Background (CMB) rest frame and Hubble's law. This places our home galaxy at a distance of approximately 26 million light years from the centre of the universe. Because we are making observations from a point relatively close to the centre of the universe, the universe appears to be isotropic and homogeneous but this is not the case. The CMB is coming from a source located within the event horizon of the universe. There is sufficient mass in the universe to create an event horizon at the Schwarzschild radius. Galaxies form over time due to the energy released by the expansion of space. Conservation of energy must consider total energy which is mass (+ve) plus energy (+ve) plus spacetime curvature (-ve) so that the total energy of the universe is always zero. The predominant position of galaxy formation moves over time from the centre of the universe towards the boundary so that today the majority of new galaxy formation is taking place beyond our horizon of observation at 14 billion light years.

Keywords: cosmology, dark energy, dark matter, evolution of the universe

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Authors: Md. Moniruzzaman

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The energy of ocean waves across a large part of the earth is inexhaustible. The whole world will benefit if this endless energy can be used in an easy way. The coastal countries will easily be able to meet their own energy needs. The purpose of this article is to use the infinite energy of the ocean wave in a simple way. i.e. a method of efficient use of wave energy. The paper starts by discussing various forces acting on a floating object and, afterward, about the method. And then a calculation for a 73.39MW hydropower from the tidal wave. Used some sketches/pictures. Finally, the conclusion states the possibilities and advantages.

Keywords: anchor, electricity, floating object, pump, ship city, wave energy

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Authors: Hussain Ali Bekhet, Endang Jati Mat Sahid

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For the past few decades, the Malaysian economy has expanded at an impressive pace, whilst, the Malaysian population has registered a relatively high growth rate. These factors had driven the growth of final energy demand. The ballooning energy demand coupled with the country’s limited indigenous energy resources have resulted in an increased of the country’s net import. Therefore, acknowledging the precarious position of the country’s energy self-sufficiency, this study has identified three main concerns regarding energy security, namely; over-dependence on fossil fuel, increasing energy import dependency, and increasing energy consumption per capita. This paper discusses the recent energy demand and supply trends, highlights the policies that are affecting energy security in Malaysia and suggests strategic options towards achieving energy security. The paper suggested that diversifying energy sources, reducing carbon content of energy, efficient utilization of energy and facilitating low-carbon industries could further enhance the effectiveness of the measures as the introduction of policies and initiatives will be more holistic.

Keywords: electricity, energy policy, energy security, Malaysia

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Authors: M. Yusefzad

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Law of energy conservation is one of the fundamental laws of physics. Energy is conserved, and the total amount of energy is constant. It can be transferred from one object to another and changed from one state to another. However, in the case of wave interference, this law faces important contradictions. Based on the presented mathematical relationship in this paper, it seems that validity of this law depends on the path of energy wave, like light, in which it is located. In this paper, by using some fundamental concepts in physics like the constancy of the electromagnetic wave speed in a specific media and wave theory of light, it will be shown that law of energy conservation is not valid in every condition and in some circumstances, it is possible to increase energy of a system with a determined amount of energy without any input.

Keywords: power, law of energy conservation, electromagnetic wave, interference, Maxwell’s equations

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Authors: Mohamad Alkhalidi, S. Neelamani, Noor Alanjari

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The main purpose of harbors and marinas is to create a calm and safe docking space for marine vessels. Standard rubble mound breakwaters, although widely used, occupy port space and require large amounts of stones or rocks. Kuwait does not have good quality stone, so they are imported at a very high cost. Therefore, there is a need for a new wave energy dissipating structure where stones and rocks are scarce. While permeable slotted vertical walls have been proved to be a suitable alternative to rubble mound breakwaters, the introduction of sloped slotted walls may be more efficient in dissipating wave energy. For example, two slotted barriers with 60degree inclination may be equivalent to three vertical slotted barriers from wave energy dissipation point of view. A detailed physical model study is carried out to determine the effects of slope angle, porosity, and a number of walls on wave energy dissipation for a wide range of random and regular waves. The results of this study can be used to improve and optimize energy dissipation and reduce construction cost.

Keywords: porosity, slope, wave reflection, wave transmission

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Authors: M. Sundaram, H. R. Sanath Kumar, A. Ramprakash

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Energy saving is a key sustainability focus area for the Indian telecom industry today. This is especially true in rural India where energy consumption contributes to 70 % of the total network operating cost. In urban areas, the energy cost for network operation ranges between 15-30 %. This expenditure on energy as a result of the lack of grid power availability highlights a potential barrier to telecom industry growth. As a result of this, telecom tower companies switch to diesel generators, making them the second largest consumer of diesel in India, consuming over 2.5 billion litres per annum. The growing cost of energy due to increasing diesel prices and concerns over rising greenhouse emissions have caused these companies to look at other renewable energy options. Even the TRAI (Telecom Regulation Authority of India) has issued a number of guidelines to implement Renewable Energy Technologies (RETs) in the telecom towers as part of its ‘Implementation of Green Technologies in Telecom Sector’ initiative. Our proposal suggests the implementation of a Programmable Logic Controller (PLC) based ‘optimisation controller’ that can not only efficiently utilize the energy from RETs but also help to conserve the power used in the telecom towers. When there are multiple RETs available to supply energy, this controller will pick the optimum amount of energy from each RET based on the availability and feasibility at that point of time, reducing the dependence on diesel generators. For effective maintenance of the towers, we are planing to implement a SCADA based monitoring system along with the ‘optimization controller’.

Keywords: operation costs, consumption of fuel and carbon footprint, implementation of a programmable logic controller (PLC) based ‘optimisation controller’, efficient SCADA based monitoring system

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Authors: Danilo Habermann, Aleksander Medella, Carla Cremon, Yusef Caceres

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This paper aims to analyze the ability of 2d point clouds features to classify different models of helicopters using radars. This method does not need to estimate the blade length, the number of blades of helicopters, and the period of their micro-Doppler signatures. It is also not necessary to generate spectrograms (or any other image based on time and frequency domain). This work transforms a radar return signal into a 2D point cloud and extracts features of it. Three classifiers are used to distinguish 9 different helicopter models in order to analyze the performance of the features used in this work. The high accuracy obtained with each of the classifiers demonstrates that the 2D point clouds features are very useful for classifying helicopters from radar signal.

Keywords: helicopter classification, point clouds features, radar, supervised classifiers

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Authors: Norshazmira Mat Azmi, Sayidal El Fatimah Masnan, Shatirah Akib

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More than 70% of the Earth is covered by oceans, which are considered to possess boundless renewable energy, such as tidal energy, tidal current energy, wave energy, thermal energy, and chemical energy. The hybrid system help in improving the economic and environmental sustainability of renewable energy systems to fulfill the energy demand. The concept of hybridizing renewable energy is to meet the desired system requirements, with the lowest value of the energy cost. This paper propose a hybrid power generation system suitable for remote area application and highlight the impact of surface waves on turbine design and performance, and the importance of understanding the site-specific wave conditions.

Keywords: marine current energy, tidal turbines, wave turbine, renewable energy, surface waves, hydraulic flume experiments, instantaneous wave phase

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Authors: Davood Karimipour

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Since long ago, Russia has been one of the most influential actors in regional equations in South West Asia. The geographic affinity of its vital interests with Western Asia has caused Moscow to have a high sensitivity to the balance of power in the Middle East, as its role in the Syrian crisis clearly demonstrated the importance. In recent years, Moscow has tried to use the energy diplomacy tool in maintaining the balance of power between the major powers in the region. The paper, based on the qualitative case study method, investigates how Russia’s energy diplomacy plays a role in the balance of regional forces in the Middle East, studying the country’s conduct towards Iran, Saudi Arabia, Turkey, and Israel. The hypothesis presented that Russia, using energy tools, is trying to push the regional powers toward cooperation in order to increase the influence in the region, increase power in global markets, and controlling the US to restore power balance in the region. Its cooperation in the Iranian gas industry, the country’s relations with Saudis in the framework of OPEC, cooperation with the Turkish Kurds and the presence in the Israeli gas industry are an example of these Russian energy diplomacy initiatives in West Asia, which is the common point of the Moscow approach to South West Asia.

Keywords: Russia, balance of power, energy diplomacy, Middle East

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Authors: Jiahui Song

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The application of an electric field can cause poration at cell membranes. This includes the outer plasma membrane, as well as the membranes of intracellular organelles. In order to analyze and predict such electroporation effects, it becomes necessary to first evaluate the electric fields and the transmembrane voltages. This information can then be used to assess changes in the pore formation energy that finally yields the pore distributions and their radii based on the Smolchowski equation. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into the pore formation energy equation. These changes make the pore formation energy E(r) self-adjusting in response to pore formation without causing uncontrolled growth and expansion. By using dynamic membrane tension, membrane electroporation in response to a 180kV/cm trapezoidal pulse with a 10 ns on time and 1.5 ns rise- and fall-times is discussed. Poration is predicted to occur at times beyond the peak at around 9.2 ns. Modeling also yields time-dependent distributions of the membrane pore population after multiple pulses. It shows that the pore distribution shifts to larger values of the radius with multiple pulsing. Molecular dynamics (MD) simulations are also carried out for a fixed field of 0.5 V/nm to demonstrate nanopore formation from a microscopic point of view. The result shows that the pore is predicted to be about 0.9 nm in diameter and somewhat narrower at the central point.

Keywords: high-intensity, nanosecond, dynamics, electroporation

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Authors: Norshazmira Mat Azmi, Sayidal El Fatimah Masnan, Shatirah Akib

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Boundless renewable energy, such as tidal energy, tidal current energy, wave energy, thermal energy and chemical energy are covered and possessed by oceans. The hybrid system helps in improving the economic and environmental sustainability of renewable energy systems to fulfill the energy demand. The objective and concept of hybridizing renewable energy is to meet the desired system requirements, with the lowest value of the energy cost. This paper reviews applications of using hybrid power generation system for remote area. It also highlights the future directions to investigate the impacts of surface waves on turbine design and performance. The importance of understanding the site-specific wave conditions could also been explored.

Keywords: hybrid, marine current energy, tidal turbine, wave turbine

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Authors: Zakariya B. H., Idris M. I., Jungudo M. A.

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High energy consumptions of urban settlements in Nigeria are escalating due to strong population growth and migration as a result of crises. The demand for lighting, heating, ventilation and air conditioning (LHVAC) is becoming higher. Conversely, there is a poor electricity supply to both rural and urban settlement in Nigeria. Generators were mostly used in Nigeria as a source of energy for LHVAC. Energy efficiency can be defined as any measure taken to reduce the amount of energy consumed for heating ventilation and air-conditioning (HVAC), and house hold appliances like computers, stoves, refrigerators, televisions etc. The aim of the study was to minimize energy consumption in building through the integration of energy efficiency and renewable energy in building sector. Some of the energy efficient buildings within the study area were identified, the study covers there major cities of Nigeria namely, Abuja, Kaduna and Lagos city. The cost of investment on the energy efficiency and renewable energy was determined and compared with other fossil energy source for conventional building. Findings revealed that the low energy and energy efficient buildings in Nigeria are cheaper than the conventional ones. Based on the finding of the research, construction stake holders are strongly encouraged to abandon the conventional buildings and consider energy efficiency and renewable energy in buildings.

Keywords: energy, efficiency, LHVAC, sustainable development

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Authors: Shafique Qadir Memon, Muhammad Safar Mirjat, Abdul Quadir Mughal, Nadeem Amjad

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The aims of this study were to determine direct input energy and indirect energy in maize production, to evaluate the inputs energy consumption and outputs energy gained for maize production in Islamabad, Pakistan for spring 2013. Results showed that grain yield was maximum under deep tillage as compared to conventional and zero tillage. Total energy input/output were maximum in deep tillage as compared to conventional tillage while lowest in zero tillage, net energy gain were found maximum under deep tillage.

Keywords: tillage, energy, grain yield, net energy gain

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Authors: S. Kreitlein, N. Eder, J. Franke

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The importance of energy efficiency within the production process increases steadily. Unfortunately, so far no tools for a comprehensive assessment of energy efficiency within the production process exist. Therefore the Institute for Factory Automation and Production Systems of the Friedrich-Alexander-University Erlangen-Nuremberg has developed two methods with the goal of achieving transparency and a quantitative assessment of energy efficiency: EEV (Energy Efficiency Value) and EPE (Energetic Process Efficiency). This paper describes the basics and state of the art as well as the developed approaches.

Keywords: energy efficiency, energy efficiency value, energetic process efficiency, production

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Authors: Ali M. EL-Soll

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Physical properties of Sarir waxy crude oil was investigated, pour-point was determined using ASTM D-79 procedure, paraffin content and carbon number distribution of the paraffin was determined using gas liquid Chromatography(GLC), polymeric additives were prepared and their structures were confirmed using IR spectrophotometer. The molecular weight and molecular weigh distribution of these additives were determined by gel permeation chromatography (GPC). the performance of the synthesized additives as pour-point depressants was evaluated, for the mentioned crude oil.

Keywords: sarir, waxy, crude, pour point, depressants

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Authors: Lina Wu, Jia Liu, Ye Li

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The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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