Wyniki wyszukiwania dla: MICROSTRIP PATCH MODIFICATION
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Photoactivity of decahedral TiO2 loaded with bimetallic nanoparticles: Degradation pathway of phenol-1- 13 C and hydroxyl radical formation
PublikacjaDecahedral TiO2decorated with bimetallic nanoparticles were synthesized via radiolysis and photode-position method. The effect of bimetallic surface composition (Ag Pt, Ag Au, Au Pd, Au Pt) as well asdeposition technique (simultaneous or sequential) on the photocatalytic activity in phenol degradationand efficiency of hydroxyl radicals generation under UV–vis light irradiation were investigated. Modifiedand pristine decahedral...
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COMPARISON OF PREDICTIVE METHODS FOR FLOW BOILING HEAT TRANSFER IN CONVENTIONAL CHANNELS AND MINICHANNELS – THE EFFECT OF REDUCED PRESSURE
PublikacjaIn the paper are presented the results of follow on studies from [1]–[3] using authors own model to predict heat transfer coefficient during flow boiling. The model has been tested against a large selection of experimental data collected from various researchers to investigate the sensitivity of the in-house developed model. The collected experimental data came from various studies from literature and were conducted for the full...
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Modeling and control of a redundantly actuated variable mass 3RRR planar manipulator controlled by a model-based feedforward and a model-based-proportional-derivative feedforward–feedback controller
PublikacjaIn the paper, dynamics of a complex mechatronics system is considered. A redundantly actuated planar manipulator is the base of the mechanical part of it. It is a 3RRR 1 platform based parallel manipulator. To control its trajectory, a model-based feedforward controller is employed. Three aspects are fundamental in the presented investigations. The first focus is on development of an accurate numerical model used to solve the inverse...
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RE-SHAPING THE LAND AND WATER CONNECTIONS AND ITS ROLE IN ACHIEVING LANDSCAPE AND ECOLOGICAL SYSTEMS’ CONTINUITY ON THE POST-INDUSTRIAL TERRITORIES
PublikacjaThis paper delves into recently applied strategies of creating new water areas and modifying the existing ones as a part of the transformation processes of post-industrial territories. It proves that while the pursuit for unique architectural and urban space values remains an important factor contributing to such modifications, they may also play an important role in reclaiming ecological systems continuity. On the basis of theoretical...
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Modelling and optimisation of MXene-derived TiO2/Ti3C2 synthesis parameters using Response Surface Methodology based on the Box–Behnken factorial design. Enhanced carbamazepine degradation by the Cu-modified TiO2/Ti3C2 photocatalyst
PublikacjaIn the present study, a hydrothermal method in a water/ethanol environment was used for the first time to obtain novel Cu/TiO2/Ti3C2 composites with high photocatalytic activity for the degradation of carbamazepine (CBZ) under simulated solar light. The Box–Behnken factorial design was coupled with Response Surface Methodology (RSM) for synthesis parameter optimisation. The effect of different synthesis parameters, including temperature, time...
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Improved-Efficacy EM-Based Antenna Miniaturization by Multi-Fidelity Simulations and Objective Function Adaptation
PublikacjaThe growing demands for integration of surface mount design (SMD) antennas into miniatur-ized electronic devices have been continuously imposing limitations on the structure dimen-sions. Examples include embedded antennas in applications such as on-board devices, picosatel-lites, 5G communications, or implantable and wearable devices. The demands for size reduction while ensuring a satisfactory level of the electrical and field...
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Low-Cost and Precise Automated Re-Design of Antenna Structures Using Interleaved Geometry Scaling and Gradient-Based Optimization
PublikacjaDesign of contemporary antennas is an intricate endeavor involving multiple stages, among others, tuning of geometry parameters. In particular, re-designing antennas to different operating frequencies, makes parametric optimization imperative to ensure the best achievable system performance. If the center frequency at the current design is distant from the target one, local tuning methods generally fail, whereas global algorithms...
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Musical inspiration in contemporary architecture - to build a music and to hear an architecture
PublikacjaThe goal of this research is chosen from a wide range of subjects within two fields of knowledge on the crossroads between music and architecture There are many designs in modern contemporary architecture that would illustrate the relationship between music and architecture, mainly through musical inspiration. The article shows contemporary musical and architectural discussion that cross over from the theoretical to the practical...
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DETERMINATION OF SURFACTANTS IN ENVIRONMENTAL SAMPLES - PART I. CATIONIC COMPOUNDS = Oznaczanie Surfaktantów W Próbkach Środowiskowych. Część I. Związki Kationowe
PublikacjaCompounds from the group of cationic surfactants are widely applied in household, industrial, cleaning, disinfectant, cosmetic and pharmaceutical products as their specific properties (antimicrobial, emulsifying, anticorrosion, softening). After use, cationic surfactants are disposed to wastewater-treatment plants and finally with effluent water to surface waters due to their incomplete degradation. Moreover, they can freely circulate...
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The role of aluminium in metal–organic frameworks derived carbon doped with cobalt in electrocatalytic oxygen evolution reaction
PublikacjaWater electrolysis is one of the most crucial processes in the development of new energy sources, where ultra-clean fuel is produced - hydrogen. Oxygen evolution reaction (OER) is the sluggish process of overall water splitting. Therefore, this study presents the design, characterization and electrochemical study of cobalt-based electrocatalysts embedded into porous carbons derived from an Al-metal–organic...
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How to Design Affect-aware Educational Systems – the AFFINT Process Approach
PublikacjaComputer systems, that support learning processes, can adapt to the needs and states of a learner. The adaptation might directly address the knowledge deficits and most tutoring systems apply an adaptable learning path of that kind. Apart from a preliminary knowledge state, there are more factors, that influence education effectiveness and among those there are fluctuating emotional states. The tutoring systems may recognize or...
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Optimal retrofit strategy using viscous dampers between adjacent RC and SMRFs prone to earthquake‑induced pounding
PublikacjaNowadays, retrofitting-damaged buildings is an important challenge for engineers. Finding the optimal placement of Viscous Dampers (VDs) between adjacent structures prone to earthquake-induced pounding can help designers to implement VDs with optimizing the cost of construction and achieving higher performance levels for both structures. In this research, the optimal placement of linear and nonlinear VDs between the 3-story, 5-story,...
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Tuning Electrochemical Performance by Microstructural Optimization of the Nanocrystalline Functional Oxygen Electrode Layer for Solid Oxide Cells
PublikacjaFurther development of solid oxide fuel cell (SOFC) oxygen electrodes can be achieved through improvements in oxygen electrode design by microstructure miniaturisation alongside nanomaterials implementation. In this work, improved electrochemical performance of an La0.6Sr0.4Co0.2Fe0.8O3-d (LSCF) cathode was achieved by the controlled modification of the La0.6Sr0.4CoO3-d (LSC) nanocrystalline interlayer introduced between a porous...
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Fracture Surface Topography Parameters for S235JR Steel Adhesive Joints After Fatigue Shear Testing
PublikacjaThis paper presents the experimental results of a study investigating the effect of holes and notches made on the overlap ends on the strength of adhesive joints. Single-lap joints made of S235JR steel sheets bonded with Araldite 2024-2 epoxy adhesive were tested. For comparative reasons, static shear strength tests and high-cycle fatigue strength tests were performed. Adhesive-filled joints having three holes, each with a diameter...
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Estimation and modeling hydrolysis of slowly biodegradable substrate based on the batch respirometric tests in activated sludge systems
PublikacjaNowadays, appropriate determination of chemical oxygen demand (COD) fractionation together with degradation kinetics of organic compounds have a prime importance on the design and operation of activated sludge systems. Batch respirometric tests based on the oxygen uptake rates (OUR) and corresponding COD is accepted method to reflect the consumption of biodegradable substrates. The influence of the readily biodegradable (Ss) fraction...
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The effect of metal cluster deposition route on structure and photocatalytic activity of mono- and bimetallic nanoparticles supported on TiO2 by radiolytic method
PublikacjaTiO2 (P25) was modified with small and relatively monodisperse mono- and bimetallic clusters (Ag, Pd, Pt, Ag/Pd, Ag/Pt and Pd/Pt) induced by radiolysis to improve its photocatalytic activity. The as-prepared samples were characterized by X-ray fluorescence spectrometry (XRF), photoluminescence spectrometry (PL), diffuse reflectance spectroscopy (DRS), X-ray powder diffractometry (XRD), scanning transition electron microscopy (STEM)...
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Biopolyols obtained via crude glycerol-based liquefaction of cellulose: their structural, rheological and thermal characterization
PublikacjaIn this work lignocellulose biomass liquefaction was used to produce biopolyols suitable for the manufacturing of rigid polyurethane foams. In order to better evaluate the mechanism of the process, pure cellulose was applied as a raw material. The effect of time and temperature on the effectiveness of liquefaction and the parameters of resulting biopolyols were characterized. The prepared materials were analyzed in terms of their...
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The influence of the Cu2O deposition method on the structure, morphology and photoresponse of the ordered TiO2NTs/Cu2O heterojunction
PublikacjaThe increased interest in highly ordered titania structures exhibiting tubular shape that could be directly formed onto the stable substrate is related with the intensive research on their modification enabling absorption of light within the wide solar spectrum and its further conversion into electric or chemical energy. Among others, formation of uniform 3D heterojunctions based on the TiO2 nanotubes attracts attention since porous...
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Simultaneous voltammetric determination of Cd2+, Pb2+, and Cu2+ ions captured by Fe3O4@SiO2 core-shell nanostructures of various outer amino chain length
PublikacjaIn the present study, we examined a novel functionalised magnetic nanoparticles Fe3O4@SiO2-Nn as a nano adsorbent for binding of Cd2+, Pb2+, Cu2+ ions in an aqueous solution. First, we obtained the nanoparticles functionalised with various carbon chains containing different number of amino groups: (3-amino)propyltriethoxysilane (Fe3O4@SiO2-N1), N-(2-aminoethyl)-3-aminopropyltrimethoxysilane (Fe3O4@SiO2-N2) and N1-(3-trimethoxysilylpropyl)diethylenetriamine...
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Influence of several biodegradable components added to pure and nanosilver-doped PMMA bone cements on its biological and mechanical properties
PublikacjaAcrylic bone cements (BC) are wildly used in medicine. Despite favorable mechanical properties, processability and inject capability, BC lack bioactivity. To overcome this, we investigated the effects of selected biodegradable additives to create a partially-degradable BC and also we evaluated its combination with nanosilver (AgNp). We hypothesized that using above strategies it would be possible to obtain bioactive BC. The Cemex...
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Efficient Method for the Concentration Determination of Fmoc Groups Incorporated in the Core-Shell Materials by Fmoc–Glycine
PublikacjaIn this paper, we described the synthesis procedure of TiO2@SiO2 core-shell modified with 3-(aminopropyl)trimethoxysilane (APTMS). The chemical attachment of Fmoc–glycine (Fmoc–Gly–OH) at the surface of the core-shell structure was performed to determine the amount of active amino groups on the basis of the amount of Fmoc group calculation. We characterized nanostructures using various methods: transmission electron microscope...
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Structural, thermal and physico-mechanical properties of polyurethane/brewers’ spent grain composite foams modified with ground tire rubber
PublikacjaIn this work, brewers’ spent grain (BSG) and ground tire rubber (GTR) waste fillers were applied as low-cost reinforcement phase in rigid polyurethane foam (PUR). PUR/BSG/GTR composites were prepared by a single step method, using polyglycerol as partial substitute of commercially available petrochemical polyols. Foaming parameters, chemical structure, dynamic mechanical properties, thermal stability, physico-mechanical properties...
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The optimization of enzyme immobilization at Au-Ti nanotextured platform and its impact onto the response towards glucose in neutral media
PublikacjaThe market of non-invasive glucose sensors is drastically growing due to increasing number of people suffering from diabetes. Therefore, there is a significant need for any improvement in the field of biosensors that can be used for monitoring glucose level in human body. In recent years the emphasis is put onto the modification of electrode material with enzymes possessing recognition centre specific towards particular molecules....
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Development of nanoscale morphology and role of viscoelastic phase separation on the properties of epoxy/recycled polyurethane blends
PublikacjaA novel and cost-effective approach towards the modification of epoxy matrix has been developed using recycled polyurethane for the first time without sacrificing any of the intrinsic properties of the resin. Polyurethane, recycled from waste foam by glycolysis process (RPU), was found to be very effective in improving the properties of the thermosetting resin based on Diglycidyl ether of bisphenol-A (DGEBA). The effect of the...
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Enzymatic cross-linking of β-lactoglobulin in solution and at air–water interface: Structural constraints
PublikacjaEffective and controlled use of cross-linking enzymes in structure engineering of food systems depends on characterization of the favorable conditions for enzyme-substrate complex and the limiting factors for the desired modification. In this respect, we analyzed the susceptibility of bovine β-lactoglobulin (BLG) to enzymatic cross-linking by Trichoderma reesei tyrosinase (TrTyr) and transglutaminase (TG). Changes in BLG molecular...
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ZnO-decorated green-synthesized multi-doped carbon dots from Chlorella pyrenoidosa for sustainable photocatalytic carbamazepine degradation
PublikacjaThe promising green synthesis of carbon dots (CDs) from microalga Chlorella pyrenoidosa was achieved using simple hydrothermal and microwave-assisted methods. Doping of nanomaterials by nonmetals (N, S, and P) was confirmed by X-ray photoelectron spectroscopy (XPS), while the existence of metals in the CDs was confirmed by inductively coupled plasma optical emission spectroscopy (ICP-OES) and transmission electron microscopy (TEM),...
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Lignocellulosic waste biosorbents infused with deep eutectic solvents for biogas desulfurization
PublikacjaThis paper introduces an innovative method for treating biogas streams, employing lignocellulosic biosorbents infused with environmentally friendly solvents known as deep eutectic solvents (DES). The primary focus of this study was the elimination of volatile organosulfur compounds (VSCs) from model biogas. Biosorbents, including energetic poplar wood, antipka tree, corncobs, and beech wood, were used, each with varying levels...
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Defected Ag/Cu-MOF as a modifier of polyethersulfone membranes for enhancing permeability, antifouling properties and heavy metal and dye pollutant removal
PublikacjaIn this study, a novel bimetallic metal-organic framework (MOF) i.e. Ag/Cu-MOF was synthesized using a solvothermal method and later incorporated at different concentrations (0.1–2 wt%) using a phase inversion method for modification and antifouling property improvement of polyethersulfone (PES) membranes. The resulting Ag/Cu-MOF characteristics were investigated using different techniques, such as FTIR, XRD, FE-SEM and EDX. The...
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Nanokrystaliczne warstwy ceramiczne otrzymywane metodą pirolizy aerozolowej w tlenkowych ogniwach paliwowych
PublikacjaNiniejsza rozprawa doktorska dotyczy badań materiałów wytwarzanych w postaci cienkich, nanokrystalicznych warstw ceramicznych metodą pirolizy aerozolowej dla zastosowań w tlenkowych ogniwach paliwowych (SOFC). Badane są trzy możliwe obszary zastosowań wytwarzanych warstw tj. osadzanie powłok ochronnych na stalowych interkonektorach dostarczających gazy do elektrody tlenowej, wytwarzanie bariery ochronnej zapobiegającej dyfuzji...
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Influence of bush wear in water lubricated marine stern tube bearings with shaft misalignment
PublikacjaWater lubricated propeller shaft bearings are frequently employed on modern ships due to their advantages such as durability, simplicity and low price. Specific working conditions on ships cause shaft misalignment which often results in rapid wearing of bush and shaft. Shaft misalignment could be an effect of manufacturing or assembly faults but sometimes it appears due to hull or shaft deformation. The wearing process has influence...
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Complex multidisciplinary optimization of turbine blading systems
PublikacjaThe paper describes the methods and results of direct optimization of turbine blading systems using a software package Opti_turb. The final shape of the blading is obtained from minimizing the objective function, which is the total energy loss of the stage, including the leaving energy. The current values of the objective function are found from 3D RANS computations (from a code FlowER) of geometries changed during the process...
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Organic pollutants photodegradation increment with use of TiO2 nanotubes decorated with transition metals after pulsed laser treatment
PublikacjaAmong various titanium(IV) oxide (TiO2, titania) structures, 1D nanotubes (TiO2 NTs) produced during the two-electrode anodization process, are extensively utilized in sensors or supercapacitors as well as in photo(electro)catalytic water splitting. However, due to wide bandgap and fast electron-hole recombination additional modifications, mostly concerned on materials surface, are required. According to the recent research, TiO2...
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Double-stage ORC system based on various temperature waste heat sources of the negative CO2 power plant
PublikacjaAnalysed is the modification of the thermodynamic cycle with the negative CO2 power plant concept by its combination with the organic Rankine cycle. The analysed power plant operates on a gas produced from the gasification of sewage sludge. The negative emission term comes from the aggregated CO2 balance resulting from the capture of the CO2, while the sewage sludge is one of the inevitable environmental sources of CO2 to be avoided....
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Electrocatalytic performance of oxygen-activated carbon fibre felt anodes mediating degradation mechanism of acetaminophen in aqueous environments
PublikacjaCarbon felts are flexible and scalable, have high specific areas, and are highly conductive materials that fit the requirements for both anodes and cathodes in advanced electrocatalytic processes. Advanced oxidative modi- fication processes (thermal, chemical, and plasma-chemical) were applied to carbon felt anodes to enhance their efficiency towards electro-oxidation. The modification of the porous anodes results in increased...
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Two small RNAs conserved in Enterobacteriaceae provide intrinsic resistance to antibiotics targeting the cell wall biosynthesis enzyme glucosamine-6-phosphate synthase
PublikacjaFormation of glucosamine-6-phosphate GlcN6P) by enzyme GlcN6P synthase (GlmS) represents the first step in bacterial cell envelope synthesis. In Escherichia coli, expression of glmS is controlled by small RNAs (sRNAs) GlmY and GlmZ. GlmZ activates the glmS mRNA by base-pairing. When not required, GlmZ is bound by adapter protein RapZ and recruited to cleavage by RNase E inactivating the sRNA. The homologous sRNA GlmY activates...
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The geometry of free-standing titania nanotubes as a critical factor controlling their optical and photoelectrochemical performance
PublikacjaTitanium dioxide nanotubes are regarded as one of the most important functional materials and due to their unique electronic properties, chemical stability and photocorrosion resistance, they find applications in, for example, highly efficient photocatalysis or perovskite solar cells. Nevertheless, modification of TiO2 nanotubes is required to overcome their main drawback, i.e. large energy bandgap (>3.2 eV) limiting their ability...
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An Easy and Ecological Method of Obtaining Hydrated and Non-Crystalline WO3−x for Application in Supercapacitors
PublikacjaIn this work, we report the synthesis of hydrated and non-crystalline WO3 flakes (WO3−x) via an environmentally friendly and facile water-based strategy. This method is described, in the literature, as exfoliation, however, based on the results obtained, we cannot say unequivocally that we have obtained an exfoliated material. Nevertheless, the proposed modification procedure clearly affects the morphology of WO3 and leads to loss...
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Electrochemically assisted deposition of hydroxyapatite on Ti6Al4V substrates covered by CVD diamond films — Coating characterization and first cell biological results
PublikacjaAlthough titaniumand its alloys are widely used as implant material for orthopedic and dental applications they show only limited corrosion stability and osseointegration in different cases. The aim of the presented research was to develop and characterize a novel surface modification system from a thin diamond base layer and a hydroxyapatite (HAp) top coating deposited on the alloy Ti6Al4V widely used for implants in contact with bone....
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Modelling of Different Aeration Modes Influencing Processes in SBR Bioreactor
PublikacjaCurrently, computer modelling together with the simulation tools tailored for that purpose constitute a very important element in planning technological changes within wastewater treatment plant. From the point of view of the WWTP operator every modification should be introduced in order to improve the quality of treated sewage with the lowest financial outlays. These requirements can be met by using computer programmes to effectuate...
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Effect of bio-polyol molecular weight on the structure and properties of polyurethane-polyisocyanurate (PUR-PIR) foams
PublikacjaThe increasing interest in polyurethane materials has raised the question of the environmental impact of these materials. For this reason, the scientists aim to find an extremely difficult balance between new material technologies and sustainable development. This work attempts to validate the possibility of replacing petrochemical polyols with previously synthesized bio-polyols and their impact on the structure and properties...
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Thermal stabilization and permanent deformation resistance of LWA/PCM-modified asphalt road surfaces
PublikacjaThis paper presents the results of attempts at reducing the problem of solar overheating of asphalt road pavement surfaces, resulting in weakening and accelerated destruction of the aforementioned structures. To protect pavement surfaces against periodic overheating, standard asphalt mixture AC 16 W 35/50, used for binder course, has been modified by replacing one of the aggregate fractions from the mineral mixture with lightweight...
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Review on robust laser light interaction with titania – Patterning, crystallisation and ablation processes
PublikacjaTitanium dioxide is regarded as a very promising semiconducting material that is widely applied in many everyday-use products, devices, and processes. In general, those applications can be divided into energy or environmental categories, where a high conversion rate, and energy and power density are of particular interest. Therefore, many efforts are being put towards the elaboration of novel production routes, and improving the...
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Nitrogen-Incorporated Boron-Doped Nanocrystalline Diamond Nanowires for Microplasma Illumination
PublikacjaThe origin of nitrogen-incorporated boron-doped nanocrystalline diamond (NB-NCD) nanowires as a function of substrate temperature (Ts) in H2/CH4/B2H6/N2 reactant gases is systematically addressed. Because of Ts, there is a drastic modification in the dimensional structure and microstructure and hence in the several properties of the NB-NCD films. The NB-NCD films grown at low Ts (400 °C) contain faceted diamond grains. The morphology...
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A new construction of shell-and-tube heat exchanger with impinging jets and minichannels technologies for heat recovery from gases – experimental analysis
PublikacjaA dynamic development of technologies allowing waste heat utilization is observed in a correspondence with a pro-ecological approach of the zero waste idea. Such approach becomes the most demanding in the area of low-temperature was heat sources, especially gaseous media. Till now, they were usually not utilized due to unfavorable thermal conditions and high costs. Therefore, the zero waste approach directs research on techniques...
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Technical and Economic Analysis of the Supercritical Combined Gas-Steam Cycle
PublikacjaCombined cycle power plants are characterized by high efficiency, now exceeding 60%. The record-breaking power plant listed in the Guinness Book of World Records is the Nishi-Nagoya power plant commissioned in March 2018, located in Japan, and reaching the gross efficiency of 63.08%. Research and development centers, energy companies, and scientific institutions are taking various actions to increase this efficiency. Both the gas...
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A new simple approach to prepare rare-earth metals-modified TiO2 nanotube arrays photoactive under visible light: Surface properties and mechanism investigation
PublikacjaApplication of Ti90RE10 alloys (RE = Ho, Er, Nd, Y, Ce, Tm) as a working electrode, instead of Ti pure foil in anodic oxidation in a fluoride-based electrolyte, resulted in formation of well-ordered nanotubes made of TiO2 and RE2O3 mixture, which could be efficiently used for pollutant removal from water and air phase upon UV and visible irradiation and easily separable from the reaction mixture to recycle. The as-prepared NTs...
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Architektura i woda - przekraczanie granic
PublikacjaPublikacja daje wgląd w procesy kształtowania połączeń wody i form zbudowanych. W obserwowanych współcześnie eksperymentach struktury budynków przeplatają się z zarysami pól wodnych, powstają konstrukcje architektoniczne unoszące się na różnego rodzaju platformach pływających. Woda jest także coraz częściej włączana w projekty urbanistyczne. Linie styku pomiędzy lądem i wodą ulegają modyfikacjom, przywraca się dawne kanały i tworzy...
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Measurement Campaign and Mathematical Model Construction for the Ship Zodiak Magnetic Signature Reproduction
PublikacjaThe paper presents the partial work done within the framework of the EDA Siramis II project focused on magnetic signature reproduction of ships. Reproduction is understood here as the ability to determine the magnetic anomaly of the local Earth magnetic field in any direction and at any measurement depth due to the presence of the analysed object. The B-91 type hydrographic ship Zodiak was selected as the real case study. The work...
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Study on polymer modified road asphalt mixture
PublikacjaThe formulation of ternary asphalt-additives blend composed of crumb rubber : low-density polyethylene (CR : LDPE) and crumb rubber : textile fiber (CR : TF) couples, and quaternary asphalt additives-blend composed of (CR : LDPE : TF) triplets on the virgin asphalt to optimize the asphalt basic and rheological properties and to use the extrusion process of two or three additives to obtain composite materials of them, as well as...
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Modal Adjustment of Rayleigh Based Structural Damping and Coordinate-Partitioning Algorithm Dedicated to Frictionless Contact Constraints between Multibody System and Structure Modelled with Finite Elements
PublikacjaThe paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations...