Computational And Mathematical Aspects Of Materials And Fluids: Fill & Download for Free

Apart from focusing on general courses on design and analysis like solid mechanics, strength of materials, pay special attention to the following courses (take them as additional if not offered as core courses):ThermodynamicsFunamentals - Basic engineering thermodynamicsApplied -Thermodynamics of power and propulsionRefrigeration and airconditioning is also important part of applied thermodynamics and is very crucial in aspects related to cooling of propulsion systems as well as controlling cabin environmentCrygenic engineering - Cryogenic engines for rocket proulsion etc.Advanced - Statistical thermodynamics and other advanced mathematical aspects of thermodynamicsFluid mechanicsFundamentals - Introduction to fluid mechanicsDynamics - Theoretical aspects of dynamics as well as computational aspects i.e. Computational Fluid dynamics CFDTurbo-machineryHeat transferIntroductory heat transfer - fundamentals of conduction, convection and radiationAdvanced - Numerical heat transferPropulsionIntroduction to aerospace propulsion and Rocket propulsionCombustionIntroduction to combustion/ Fuels and combustion etc.Turbulence and combustion modelingMathematics/computationalNumerical analysis and Linear algebraComputational methods for engineers and scientistsCFD (already mentioned above) and Finite element methods (FEM)Lab/practical courses etc.Applied thermodynamics and IC engines labFluid mechanics and turbo-machinery labHeat transfer labI did my 5-year dual-degree (B.Tech. + M.Tech.) in mechanical engineering from IIT Bombay with a specialization in Thermal and Fluids Engineering. I also obtained a minor degree in Aerospace engineering.My master’s thesis was on Investigation of combustion in liquid propellant rocket engines. Currently I am a graduate student in Mechanical engineering working in the field of Combustion and Propulsion.These are the courses that I took (except FEM) during my 5 year dual degree program. You can also chose your B.Tech. Project in the field of propulsion.Hope this helps.

All sorts!Pixar's technology is an awesome intersection of many branches of mathematics and computer science.I'd even venture to say that "intersection" doesn't quite do justice to the depth and breadth of mathematics involved; it is more like a "union" of the whole spectrum of CS research topics (from software engineering all the way to abstract math), with lots of statistics and physics.Consider the following still from their latest film, Inside Out.What kind of maths might go into a clip such as this?1. RenderingThe metaphor typically used is a camera pointing at a 3D scene, and the camera "renders" what it "sees" into a 2D image. We need to compute all the light arriving at the camera lens from the scene.The following integral describes the "rendering" equation, which is a recursive definition for how light moving away from a point in a given direction is the sum of how much light it's emitting in that direction, plus a subtended fraction of how much light it is reflecting from every other point in the universe.This precise definition is unhelpful in practice because there are infinite points and infinite recursion, which computers are no good at (but apparently nature is - curious to think about if you like to philosophize about these things).Instead, we approximate the rendering equation using statistical techniques. As a personal note, computer graphics is actually a really fun and intuitive way to learn many statistics concepts like MCMC methods, importance sampling, statistical mechanics, and the bias-variance tradeoff.Physics goes in here too. Light is not a scalar quantity - it has polarization and one needs to decide what basis to represent light in (do we use RGB basis vectors? do we allow color values greater than 255?).A great deal of computer science and engineering optimizations go into this as well.2. SimulationOk, so we can draw pictures, but we still need to know what to draw.In the above picture, Sadness (the character) is floating on a pillow cushion atop some molten lava. She's wearing a fuzzy sweater, and as she speaks, her face deforms in motion.For something with complex behavior like lava, it may be easier to simulate it rather than have an artist animate its fluid advection behavior. Before we draw a picture of physical reality, we often need to simulate physical reality itself.The sweater is made of cloth, which behaves somewhat like a dampened system of springs (where each sweater thread is a spring). That has to be simulated so it behaves like a sweater when Sadness is moving.Sadness's hair is also a system of springs that absorbs kinetic energy from the movement of her head, and is influenced by wind.The lava gives off light (which feeds into the light transport simulation). If the lava model was built from first principles, we might actually calculate the light using the amount of blackbody radiation emitted by molten rock.This might be unnecessary though, if the shading artist simply decides on the emission color ahead of time.Note that Pixar is not in the business of making perfectly realistic renderings, but of touching hearts and making money. Having the ability to push the limits on how many lights and how pretty the images can be affords artists with ever more creative room, so that's why Pixar invests heavily in math/tech.3. Scene RepresentationAs mentioned in Khan Academy's "Pixar In a Box" Layout section, representation of scene geometry is done using a lot of linear algebra. Whether it is modelers tweaking some vertices on a characters face mesh or a set dresser arranging some item, stuff needs to get moved around, or "transformed". These "transformations" are represented using linear algebra.Rotations, transformations, and scalings are simple, but linear algebra is also involved in inverse kinematics problems (e.g. animation) and numerical solvers for simulation (i.e. finding solutions to large systems of equations for numerical solutions to spring mechanics, or preserving volumes when Sadness's cheeks are squished).From time to time, an object might fall and collide with some other objects. The collision of meshes has to be simulated too. More numerical methods, and if the colliding objects are squishy, finite element methods might be needed.4. ShadingHand-in-hand with rendering is shading, which describes how every little patch of geometry in the scene responds to incoming light. Again, we're trying to simulate reality here.A bumpy or even fuzzy surface is noticeably distinct from a flat surface because of how it reflects light. Surfaces in reality are a lot bumpier and heterogenous (in composition) than the computer models, so this geometry is compensated for by shading.What is a good way to approximate a variety of different surfaces?Machine learning, linear regression and other parametric models come into play here, and a BSSDF models are another active area of research.In fact, with enough data, machine learning methods can actually be used to do regression on the light field equation itself - that is, make a "guess" as to what the light integral turns out to be, without even doing full path tracing.These fitted models may be statistical distributions themselves - a microfacet model that can be used to produce shimmery, mesoscopic reflectance behavior of knitted sweaters or hair or skin.Observe the pictures below - they look fuzzy, right?Surprisingly, these are just primitive cubes and tori, without a single strand of fur geometry. These images are shaded by sampling from the statistical distribution of how an actual fuzzy object would react to light, and it turns out that reproducing the statistics of an objects' behavior can serve as a very good impression of the underlying object (the fur geometry). I think that's pretty profound.Source: https://www.cs.drexel.edu/~david/Classes/CS586/Papers/p271-kajiya.pdfComputer graphics facilitates a lot of interesting combinations of maths you might not see in other places.5. Miscellaneous GeometryBasic things like parabolas and splines and fractals turn up everywhere in computer graphics, whether to draw simple curved geometries like grass in a large-scale, parametric fashion, or even the smooth motion curves of a joint animation over time.6. Differential Geometry and TopologyKeenan Crane does a lot of really cool work in this area. I don't understand a lot of it myself, but it appears to have really huge computational complexity improvements and make feasible certain angle-preserving mesh operations (like deforming a rabbit into a ball) that weren't possible before using traditional representations of meshes.7. Signal ProcessingAll of the emotions' avatars are made out of shimmery material This undoubtedly presents some aliasing difficulties in images, so anti-aliasing methods must be used. Anti-aliasing is also an important part of rendering (see http://iquilezles.org/www/articles/filtering/filtering.htm), which brings up interesting questions on whether aliasing has a deeper meaning with regards to monte carlo estimates of light transport.The notion of spatial frequency is also important from an artistic standpoint, as compositions with a spectrum of spatial frequencies tend to be more visually compelling (see http://iquilezles.org/www/articles/multiresaocc/multiresaocc.htm)Set dressers will intersperse a scene with large blocks, followed by progressive refinement at higher levels (frequencies) of detail. This can also be done procedurally, whereby multiple octaves of spatial frequencies are composed together to produce the "impression" of phenomena like hair, shrubs, etc.Summary and more resourcesAll told, computer graphics span a lot of mathematics because the holy grail of graphics is to simulate all of physical reality (light, fluids, collisions), as fast as possible (CS algorithms and data structures).The Pixar-in-a-Box curriculum is a nice start to understand how computer graphics plays a direct role in the more common operations. Pixar in a BoxFor more advanced mathematical concepts, Ke-Sen Huang maintains on his homepage (http://kesen.realtimerendering.com/) listings of papers presented at the annual SIGGRAPH conference (Special Interest Group on GRAPHics and Interactive Techniques) and other graphics conferences. These really widen the rabbit hole of mathematics. Topics can vary from year to year, but areas of research include differential geometry, optimization, numerical methods.Disney research does cool work as well: Paper Generators: Harvesting Energy from Touching, Rubbing and SlidingI've only mentioned the mathematical aspects of CG and the work relevant to Pixar. There's also lots of Computer Science and user-interaction research.

The Department of Chemical Engineering across various universities globally have the following concentration/thrust areas for research which are listed below.Colloid and Interface ScienceColloid and interface science deals with multi-phase systems in which one or more phases are dispersed in a continuous phase of different composition or state. Classical colloid science deals with dispersions for which at least one dimension of a dispersed phase falls within about 1 and 1000 nm. In applied colloid science the upper size limit is commonly extended to at least 10,000 to 100,000 nm. Interface science deals with dispersions in which there is an extremely large interfacial area between two of the phases. The dispersed phases may be particles, droplets, or bubbles.This area holds a lot of importance in industrials, environmental, biomedical and biotech applications.The applications include applications include detergency, emulsification, and wetting; adhesives, coatings, and thin films; petrochemical processes; food, paint, pharmaceutical, cosmetic, and photographic technologies; controlled-release of active ingredients in pharmaceuticals and consumer products; removal of trace contaminants from water sources; bioseparations; and biomedical applications including skin irritation and mitigation, and transdermal and oral drug delivery.Some of the systems that can be studied are micellar solutions (surfactant-water systems), solutions of nanoparticles and surfactants, polymer-surfactant systems,pharmaceutical drugs, aerosols etc.Catalysis and Reaction EngineeringSo we know chemical reactions occur. But how can a reaction yield maximum product? How does it occur in an industry? The answer by all means lies in studying reactor design and reaction kinetics.Chemical reactions lie in the heart of processes where molecules are transformed from raw materials to useful products. For the efficient and economic utilisation of such chemical transformations the domain where they are performed (the reactor) needs to be carefully designed accounting for kinetics, hydrodynamics, mass and heat transfer. Catalysis plays a significant role in many of these transformations, leading to more efficient, greener and more sustainable processing routes.Often this area is integrated with a Surface Chemistry group too. This helps to study how reactions occur on the surface of catalysts.Quite a lot is being studied about reactions in microreactors these days.Some of the other interest areas include photocatalysis, electrocatalysis, catalytic pyrolysis etc.Polymers and materialsPolymers are versatile because their properties are so wide-ranging. The versatility becomes more profound in the copolymers made from multiple precursors, and polymers compounded with filler materials. Research in polymers encompasses the chemical reactions of their formation, methods of processing them into products, means of modifying their physical properties, and the relationship between the properties and the underlying molecular and solid phase structure.As for Materials, either it can be studied as one of the research areas in Chemical Engineering or one could opt for the vast field of Materials Science and Engineering for the same.In any case, inorganic materials that are found in nature form the basis for new materials which are used in novel applications due to their electronic, mechanical and optical properties.Thin films are studied which find applications in fuel cells, a source of alternative energy being widely studied across the globe.Nanomaterials are a special class of materials that can be studied as the properties of such materials can be tuned as per requirement.Biomaterials are also being studied extensively as new materials for biological applications are being generated from biological molecules.Transport PhenomenaDescriptions of transport of momentum, energy, and species, often accompanied by chemical reaction – i.e. fluid mechanics, heat transfer, mass transfer, and reaction engineering – are one of the central and most successful paradigms of modern chemical engineering.Modern research in transport processes addresses problems through combinations of theory, computation, and experiment.Some of the studies in this field include Dynamics of Complex Multiphase materials such as three phase fluid systems and granular materials, Non-Newtonian flow properties of complex fluid systems, problems involving mixing and blending of multiphase polymers and polymer-inorganic nanocomposites. In some universities, emulsions in drug-delivery and food processing are also studied as a part of Transport Phenomena. Microfluidic flow systems, mass transfer and heat transfer in nanostructures are some of the other areas of concentration in Transport Phenomena.Modeling, Theory and SimulationComputational power is changing the nature of science and engineering research in today's world. Modeling and simulation can help in cutting cost by focusing experiments on critical areas and creating frameworks in which diverse experimental results can be seen in a coherent picture.This research focus, thus, deals with computational aspects of complex systems covering modelling, simulation, control and optimization.Studies can be conducted on process control and monitoring with applications in large scale chemical plants, model- based control and monitoring of hybrid process systems with applications to chemical processes and biological networks. Computer simulations can also be used to understand how microscopic properties of materials influence macroscopic behavior.Modeling and simulation can also be done at the molecular and nano scale. In this case, fundamental principles of statistical mechanics and quantum theory are coupled with modern computing tools to derive atomistic descriptions of materials structure, materials properties, and a wide range of solid state and fluid phase physico-chemical phenomena.Process Design and Process EngineeringIn chemical engineering, process design is the design of processes for desired physical and/or chemical transformation of materials. Process design is central to chemical engineering, and it can be considered to be the summit of that field, bringing together all of the field's components.Process design can be the design of new facilities or it can be the modification or expansion of existing facilities. The design starts at a conceptual level and ultimately ends in the form of fabrication and construction plans. The documentation of the design can be done by preparing Block Flow Diagrams, Process Flow Diagrams or Piping and Instrumentation Diagrams.The Design of the process is made with the aid of mathematical tools that simulate the process and obtain optimum conditions for operation.Use of simulation in design allows the identification of dangerous operating regions and testing of accident conditions.During process design, economic analysis and feasibility of the process must also be analysed.Some of the areas that one can look into for process engineering are multiscale process operations and control, nanoscale process systems engineering, biochemical process engineering and process optimization.Alternate EnergyOne of those areas where a lot of money is being spent globally to find new and alternate sources of energy.The research themes in this area include, batteries, fuel cells, biofuels, solar energy, carbon dioxide capture and sequestration, hydrogen storage and conversion.Food Science and TechnologyFood Science or Bromatology is a branch of applied Sciences. It is a discipline in which engineering, biological and physical sciences are combines to study the nature of foods, causes of deterioration, underlying food processing principles, and improvement of food products for public consumption.Food industry is practically the largest industry in the world and needs professionals who will be developing food and beverages in response to the needs and demands of the society.There are ample career opportunities in this field as there are less number of graduates than there are positions available to them in the industry.So, what are the areas that you can study in this field?1. Sensory Science- This area primarily involves new product development, creating new tastes and flavors, develop more nutritous food items. It also involves tasting of a new food product, trying to identify what is desirable and what is not. Hence, this involves a lot of work with trained experts and consumers and interaction with them.2.Food Chemistry- It teaches you to understand the structure and function of food ingredients and how to make food healthier for consumption. This is the area where chemistry comes into picture and you learn to ensure product stability, consistent flavor and texture and ease of processing the food items.3. Microbiology- Microbes are all around us and so are they present in our food items. Thus it is necessary to ensure that the food products are safe for consumption. So, this field teaches you to ensure the safety of food supply right from initial storage through processing, transportation and retail channels, until the consumer purchases the item. Therefore, one develops processes, monitors conditions and tests foods for contamination.4. Engineering- Packaging foods in a way their shelf life is extended, flavor and nutrition is preserved and is appealing to the customers falls in the domain of work of an engineer. An engineer is also responsible for developing processes to ensure product quality and maximising process efficiency.5. Fermentation Science- It involves the creation of wines, beers, and fermented food products. It is an ancient art, combined with modern science. It's all the aspects of food science—sensory science, food chemistry, microbiology, and engineering, focused in on a specific set of products. Fermentation scientists know how to analyze ingredients, how to monitor processes, how to adjust procedures to obtain a desired outcome—and how to create a product that is appealing to the consumer.Nanoscience and NanotechnologyDown to Nano Follow the link above to know everything about Nano.Petroleum EngineeringPetroleum engineering is a field of engineering concerned with the activities related to the production of hydrocarbons, which can be either crude oil or natural gas. Typically, a petroleum engineering graduate is given the job to discover natural sources of oil and examine the same. Similarly, developing the latest machines and equipments which can be used in the extraction and processing of oil is part of the job of a petroleum engineer. Petroleum engineers have global career and are hired by global oil companies. The petroleum Engineering is divided into two parts.Upstream SectorThe upstream sector consists of activities like exploration, production and exploitation of oil and natural gases. After gaining a qualification in petroleum engineering, the engineers work in the exploration and production activities of petroleum and other related products. Using the latest drilling technology and geophysics for the exploration of oil reservoirs, they exploit the same for maximum output.Downstream SectorThe downstream sector consist activities such as the refining, marketing and distributing of petroleum products. Production is not the only work carried out in a petroleum company and the job of petroleum engineer does not get over as the oil is produced, rather, it starts at this stage. Refining process is crucial for an oil product as then only it can be used. Marketing and distributing department may require a petroleum engineer to have some management degree.Petroleum engineers divide themselves into two types:1.Reservoir engineers work to optimize production of oil and gas via proper well placement, production rates, and enhanced oil recovery techniques.2.Drilling engineers manage the technical aspects of drilling exploratory, production and injection wells.3.Production engineers, including subsurface engineers, manage the interface between the reservoir and the well, including perforations, sand control, downhole flow control, and downhole monitoring equipment; evaluate artificial lift methods; and also select surface equipment that separates the produced fluids (oil, natural gas, and water).Environmental EngineeringEnvironmental Engineering is often offered as a part of civil engineering department or as a part of the Chemical Engineering department.It is the integration of science and engineering principles to improve the natural environment (air, water, and/or land resources), to provide healthy water, air, and land for human habitation (house or home) and for other organisms, and to remediate pollution sites. Further more it is concerned with finding plausible solutions in the field of public health, such arthropod-borne diseases, implementing law which promote adequate sanitation in urban, rural and recreational areas. It involves waste water management and air pollution control, recycling, waste disposal, radiation protection, industrial hygiene, environmental sustainability, and public health issues as well as a knowledge of environmental engineering law. It also includes studies on the environmental impact of proposed construction projects.Environmental engineers study the effect of technological advances on the environment. To do so, they conduct hazardous-waste management studies to evaluate the significance of such hazards, advise on treatment and containment, and develop regulations to prevent mishaps. Environmental engineers also design municipal water supply and industrial wastewater treatment systems as well as address local and worldwide environmental issues such as the effects of acid rain, global warming, ozone depletion, water pollution and air pollution from automobile exhausts and industrial sources. Environmental "chemical" engineers, focus on environmental chemistry, advanced air and water treatment technologies and separation processes.Scope of environmental engineeringSolid Waste ManagementEnvironmental impact assessment and mitigationWater supply and treatmentWaste heat conveyance and causeAir pollution managementBiotechnologyBiotechnology is the use of living systems and organisms to develop or make useful products. Biotechnology finds application in agriculture, food production and medicine. Over the last couple of centuries, biotechnology has expanded to include genomics, recombinant gene technologies, applied immunology and development of pharmaceutical therapies and diagnostic tests.The fact that living organisms have evolved such an enormous spectrum of biological capabilities means that by choosing appropriate organisms it is possible to obtain a wide variety of substances, many of which are useful to man as food, fuel and medicines. Over the past 30 years, biologists have increasingly applied the methods of physics, chemistry and mathematics in order to gain precise knowledge, at the molecular level, of how living cells make these substances. By combining this newly-gained knowledge with the methods of engineering and science, what has emerged is the concept of biotechnology which embraces all of the above-mentioned disciplines.Biotechnology has already begun to change traditional industries such as food processing and fermentation. It has also given rise to the development of a whole new technology for industrial production of hormones, antibiotics and other chemicals, food and energy sources and processing of waste materials. This industry must be staffed by trained biotechnologists who not only have a sound basis of biological knowledge, but a thorough grounding in engineering methods.The different terms that have been coined to identify the different applications of biotechnology are:1. Bioinformatics is an interdisciplinary field which addresses biological problems using computational techniques, and makes the rapid organization and analysis of biological data possible. The field may also be referred to as computational biology, and can be defined as, conceptualizing biology in terms of molecules and then applying informatics techniques to understand and organize the information associated with these molecules, on a large scale. Bioinformatics plays a key role in various areas, such as functional genomics, structural genomics, and proteomics, and forms a key component in the biotechnology and pharmaceutical sector.2. Blue biotechnology describes the marine and aquatic applications of biotechnology.3.Green biotechnology is biotechnology applied to agricultural processes. An example would be the selection and domestication of plants via micropropagation. Another example is the designing of transgenic plants to grow under specific environments in the presence (or absence) of chemicals. One hope is that green biotechnology might produce more environmentally friendly solutions than traditional industrial agriculture.4. Red biotechnology is applied to medical processes. Some examples are the designing of organisms to produce antibiotics, and the engineering of genetic cures through genetic manipulation.5.White biotechnology, also known as industrial biotechnology, is biotechnology applied to industrial processes. An example is the designing of an organism to produce a useful chemical. Another example is the using of enzymes as industrial catalysts to either produce valuable chemicals or destroy hazardous/polluting chemicals.So what kind of applications are we looking at?1. MedicineDrug productionPharmacogenomics-study of how genetic inheritance affects an individual's response to drugsGenetic testing for examination of DNA molecule to identify mutated sequences.Gene therapy- a technique than can be used to treat or even cure genetic and acquired diseases like cancer and AIDSHuman Genome ProjectCloning2. AgricultureCrop yieldReduced vulneraility of crops to environmental stressesImproved texture and taste or appearance of foodReduced dependance on fertilizers, pesticides and other agrochemicalsProduction of novel substances in crop plantsAnimal biotechnology3. Biological engineeringBiotechnologists are employed to scale up bioprocesses from the laboratory to manufacturing scale. It includes branches like biochemical engineering, biomedical engineering, bio-system engineering and bio process engineering etc. It is a field which has an integrated approach of fundamental biological sciences and traditional engineering principles.4. Marine biotechnologyIt is an emerging field encompassing marine biomedicine (new pharmaceuticals discovery), materials technology, bioremediation, marine biomedical model organisms, molecular genetics, genomics, bioinformatics and much more. The fundamental enthusiasm for this discipline is clearly derived from the enormous biodiversity and genetic uniqueness of life in the sea. Thirty four of the 36 fundamental Phyla of eukaryotes are found in the world's oceans. Many of these life forms, such as those that reside in the deep oceans, are poorly known.Materials Science and EngineeringMaterials Science is also known as Materials Engineering. It is an interdisciplinary applying the properties of matter to science and engineering. It incorporates principles of applied physics and chemistry. With significant media attention focused on nanoscience and nanotechnology in recent years, materials science is becoming more widely known as a specific and unique field of science and engineering. As a result, it has been propelled to the forefront at many universities.Materials Science and Engineering encompasses all natural and man-made materials – their extraction, synthesis, processing, properties, characterization, and development for technological applications. Advanced engineering activities that depend upon optimized materials include the medical device and healthcare industries, the energy industries, electronics and photonics, transportation, advanced batteries and fuel cells, and nanotechnology. Students in materials science and engineering develop a fundamental understanding of materials at the nano, micro and macro scales, leading to specialization in such topics as: biomaterials; chemical and electrochemical materials science and engineering; computational materials science and engineering; electronic, magnetic and optical materials; and structural materials.This field not only involves the study of different class of materials but also their synthesis and analysis techniques. There are various ways in which materials can be characterized such as Electron Microscopy, X-ray diffraction, calorimetry, Nuclear Magnetic Resonance, Photoluminescence, Electron diffraction. A student of materials Science has the opportunity to study and get hands-on experience with these analysis techniques.The sub disciplines of materials science are:Biomaterials – materials that are derived from and/or used with biological systems.Ceramography – the study of the microstructures of high-temperature materials and refractories, including structural ceramics such as RCC, polycrystalline silicon carbide and transformation toughened ceramicsCrystallography – the study of regular arrangement of atoms and ions in a solid, the defects associated with crystal structures such as grain boundaries and dislocations, and the characterization of these structures and their relation to physical properties.Electronic and magnetic materials – materials such as semiconductors used to create integrated circuits, storage media, sensors, and other devices.Forensic engineering – the study of how products fail, and the vital role of the materials of constructionForensic materials engineering – the study of material failure, and the light it sheds on how engineers specify materials in their productGlass science – any non-crystalline material including inorganic glasses, vitreous metals and non-oxide glasses.Materials characterization – such as diffraction with x-rays, electrons, or neutrons, and various forms of spectroscopy and chemical analysis such as Raman spectroscopy, energy-dispersive spectroscopy (EDS), chromatography, thermal analysis, electron microscope analysis, etc., in order to understand and define the properties of materials. See also List of surface analysis methodsMetallography - Metallography is the study of the physical structure and components of metals, typically using microscopy.Metallurgy – the study of metals and their alloys, including their extraction, microstructure and processing.Microtechnology – study of materials and processes and their interaction, allowing microfabrication of structures of micrometric dimensions, such as Microelectromechanical systems (MEMS).Nanotechnology – rigorously, the study of materials where the effects of quantum confinement, the Gibbs–Thomson effect, or any other effect only present at the nanoscale is the defining property of the material; but more commonly, it is the creation and study of materials whose defining structural properties are anywhere from less than a nanometer to one hundred nanometers in scale, such as molecularly engineered materials.Rheology – Some practitioners consider rheology a sub-field of materials science, because it can cover any material that flows. However, modern rheology typically deals with non-Newtonian fluid dynamics, so it is often considered a sub-field of continuum mechanics. See also granular material.Surface science/catalysis – interactions and structures between solid-gas solid-liquid or solid-solid interfaces.Textile reinforced materials – materials in the form of ceramic or concrete are reinforced with a primarily woven or non-woven textile structure to impose high strength with comparatively more flexibility to withstand vibrations and sudden jerks.Tribology – the study of the wear of materials due to friction and other factors.Sourec- Edulix