The simple layer potential for the biharmonic equation in n variables

Display Method:. Title Author Keyword. Current Issue. Evolution of vortices in the wake of an ARJ21 airplane: Application of the lift-drag model. Abstract: Wake separation is crucial to aircraft landing safety and is an important factor in airport operational efficiency.

The near-ground evolution characteristics of wake vortices form the foundation of the wake separation system design. In this study, we analysed the near-ground evolution of vortices in the wake of a domestic aircraft ARJ21 initialised by the lift-drag model using large eddy simulations based on an adaptive mesh.

Evolution of wake vortices formed by the main wing, flap and horizontal tail was discussed in detail. The horizontal tail vortices are the weakest and dissipate rapidly, whereas the flap vortices are the strongest and induce the tip vortex to merge with them. The horizontal tail and flap of an ARJ21 do not significantly influence the circulation evolution, height change and movement trajectory of the wake vortices. The far-field evolution of wake vortices can therefore be analysed using the conventional wake vortex model.

A modified Lin equation for the energy balance in isotropic turbulence. Abstract: At sufficiently large Reynolds numbers, turbulence is expected to exhibit scale-invariance in an intermediate "inertial" range of wavenumbers, as shown by power law behavior of the energy spectrum and also by a constant rate of energy transfer through wavenumber.

However, there is an apparent contradiction between the definition of the energy flux i. A: Math. In this paper we consider the more general implications of that procedure for the spectral energy balance equation, also known as the Lin equation. It is argued that the resulting modified Lin equations and their corresponding Navier-Stokes equations offer a new starting point for both numerical and theoretical methods, which may lead to a better understanding of the underlying energy transfer processes in turbulence.

In particular the filtered partitioned transfer spectra could provide a basis for a hybrid approach to the statistical closure problem, with the different spectra being tackled using different methods. Interactions of human islet amyloid polypeptide with lipid structure of different curvatures. Abstract: Curvature is one of the most important features of lipid membranes in living cells, which significantly influences the structure of lipid membranes and their interaction with proteins.

Taken the human islet amyloid polypeptide hIAPPan important protein related to the pathogenesis of type II diabetes, as an example, we performed molecular dynamics MD simulations to study the interaction between the protein and the lipid structures with varied curvatures. We found that the lipids in the high curvature membrane pack loosely with high mobility. The hIAPP initially forms H-bonds with the membrane surface that anchored the protein, and then inserts into the membrane through the hydrophobic interactions between the residues and the hydrophobic tails of the lipids.

Our result provided important insights into the mechanism of the membrane curvature-dependent property of proteins with molecular details. Investigation of Agave cantala -based composite fibers as prosthetic socket materials accounting for a variety of alkali and microcrystalline cellulose treatments.

Abstract: This study was aimed to determine the mechanical strength of composites made from Agave cantala with an unsaturated polyester matrix and microcrystalline cellulose. Cantala fiber was tested by X-ray diffraction.Interested in studying at Northumbria? With 31, students, Northumbria is one of the largest universities in the country, offering courses on either a full-time, part-time or distance learning basis.

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Navier–Stokes equations

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At the heart of each Northumbria campus, our libraries provide a range of study space and technology to suit every learning style. One of the main aims of the course is to stimulate your scientific curiosity and help you to develop you into a problem solver and a flexible thinker. Mathematics graduates are highly sought after in a variety of sectors, both in the UK and internationally, including the financial sector and public sector, as well as in commerce, industry and teaching.

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities. Additional Requirements: There are no additional requirements for this course. International Qualifications: We welcome applicants with a range of qualifications from the UK and worldwide which may not exactly match those shown above. If you have taken qualifications outside the UK you can find out how your qualifications compare by visiting our country page www.

You can find details of acceptable tests and the required grades you will need in our English Language section. Visit www. If you have qualifications from outside the UK, find out what you need by visiting www. You can find details of acceptable tests and the required grades in our English Language section: www.Interested in studying at Northumbria? With 31, students, Northumbria is one of the largest universities in the country, offering courses on either a full-time, part-time or distance learning basis.

Students from all over the world choose Northumbria University for many reasons; our academic excellence, and that they will benefit from a fantastic student experience. The world is changing faster than ever before. The future is there to be won by organisations who find ways to turn todays possibilities into tomorrows competitive edge. In a connected world, collaboration can be the key to success.

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Northumbria is a research-rich, business-focused, professional university with a global reputation for academic quality. Northumbria University is based in the heart of Newcastle upon Tyne, which is regularly voted the best place in the UK for students who are attracted by our excellent academic reputation, our top 10 graduate employment record and our outstanding campus and sports facilities.

Northumbria University Alumni Association ensures our graduates stay in touch with news from the University and fellow alumni. Its free to join for graduates of Northumbria University and our constituent colleges.

Enter your details to receive an email with a link to a downloadable PDF of this course and to receive the latest news and information from Northumbria University. To see the University's privacy policy please click here. Research strengths in areas such as quantum devices, smart and nano materials, soft matter, chaos theory and dynamical systems underpin our Physics course.

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They are sometimes accompanied by an equation of state relating pressuretemperature and density. The difference between them and the closely related Euler equations is that Navier—Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier—Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure e.

The Navier—Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currentswater flow in a pipe and air flow around a wing.

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The Navier—Stokes equations, in their full and simplified forms, help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. Coupled with Maxwell's equationsthey can be used to model and study magnetohydrodynamics.

The Navier—Stokes equations are also of great interest in a purely mathematical sense. Despite their wide range of practical uses, it has not yet been proven whether smooth solutions always exist in three dimensions — i. This is called the Navier—Stokes existence and smoothness problem. The solution of the equations is a flow velocity. It is a vector field —to every point in a fluid, at any moment in a time interval, it gives a vector whose direction and magnitude are those of the velocity of the fluid at that point in space and at that moment in time.

It is usually studied in three spatial dimensions and one time dimension, although the two spatial dimensional and steady-state cases are often useed as a model, and higher-dimensional analogues are studied in both pure and applied mathematics.

Once the velocity field is calculated, other quantities of interest such as pressure or temperature may be found using dynamical equations and relations. This is different from what one normally sees in classical mechanicswhere solutions are typically trajectories of position of a particle or deflection of a continuum.

Studying velocity instead of position makes more sense for a fluid; however for visualization purposes one can compute various trajectories. In particular, the streamlines of a vector field, interpreted as flow velocity, are the paths along which a massless fluid particle would travel.

These paths are the integral curves whose derivative at each point is equal to the vector field, and they can represent visually the behavior of the vector field at a point in time.

The Navier—Stokes momentum equation can be derived as a particular form of the Cauchy momentum equationwhose general convective form is. In this form, it is apparent that in the assumption of an inviscid fluid -no deviatoric stress- Cauchy equations reduce to the Euler equations. This is often written: [4]. The left side of the equation describes acceleration, and may be composed of time-dependent and convective components also the effects of non-inertial coordinates if present.

The right side of the equation is in effect a summation of hydrostatic effects, the divergence of deviatoric stress and body forces such as gravity. All non-relativistic balance equations, such as the Navier—Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation.

By expressing the deviatoric shear stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the above Cauchy equations will lead to the Navier—Stokes equations below. A significant feature of the Cauchy equation and consequently all other continuum equations including Euler and Navier—Stokes is the presence of convective acceleration: the effect of acceleration of a flow with respect to space.

While individual fluid particles indeed experience time-dependent acceleration, the convective acceleration of the flow field is a spatial effect, one example being fluid speeding up in a nozzle.Association Discovery can also be used for other purposes such as early detection of failures or incidents, intrusion detection, web mining, or biotechnology. Note that traditionally association discovery look for co-occurrence and do not consider the order in which an item appear within an itemset.

Associations can handle categorical, text and numeric fields as input fields: You can create an association selecting which fields from your dataset you want to use. You can also list all of your associations. This can be used to change the names of the fields in the association with respect to the original names in the dataset or to tell BigML that certain fields should be preferred. All the fields in the dataset Specifies the fields to be considered to create the association.

A value less than 1 represents the percentage of the support, and will be multiplied by the total number of instances and rounded up. Example: true name optional String,default is dataset's name The name you want to give to the new association. Each must contain, at least the field, and both operator and value. See the description below the table for more details.

the simple layer potential for the biharmonic equation in n variables

Example: "lift" seed optional String A string to be hashed to generate deterministic samples. The individual predicates within the array are OR'd together to produce the final predicate. The above examples in the arguments table specifies that the right-hand side of all discovered rules must be either the item corresponding to species is Iris-setosa and petal width within the interval (1. When a predicate for a numeric field is given, the field will be discretized along bin edges specified by the predicate.

With the above example, the field petal width will be discretized into three bins, corresponding to the values 2. If a predicate is given without an operator or value, then any item pertaining to this field is accepted into the RHS.

Discretization is used to transform numeric input fields to categoricals before further processing. You can also use curl to customize a new association. Once an association has been successfully created it will have the following properties. Creating an association is a process that can take just a few seconds or a few days depending on the size of the dataset used as input and on the workload of BigML's systems.

Navier–Stokes equations

The association goes through a number of states until its fully completed. Through the status field in the association you can determine when the association has been fully processed and ready to be used to create predictions. Thus when retrieving an association, it's possible to specify that only a subset of fields be retrieved, by using any combination of the following parameters in the query string (unrecognized parameters are ignored): Fields Filter Parameters Parameter TypeDescription fields optional Comma-separated list A comma-separated list of field IDs to retrieve.

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To update an association, you need to PUT an object containing the fields that you want to update to the association' s base URL. Once you delete an association, it is permanently deleted.

the simple layer potential for the biharmonic equation in n variables

If you try to delete an association a second time, or an association that does not exist, you will receive a "404 not found" response. However, if you try to delete an association that is being used at the moment, then BigML. To list all the associations, you can use the association base URL. By default, only the 20 most recent associations will be returned. You can get your list of associations directly in your browser using your own username and API key with the following links.

You can also paginate, filter, and order your associations. Topic Models Last Updated: Monday, 2017-10-30 10:31 A topic model is an unsupervised machine learning method for unveiling all the different topics underlying a collection of documents.

BigML uses Latent Dirichlet allocation (LDA), one of the most popular probabilistic methods for topic modeling.Enter your registered Microsoft Account or corporate account, Select the desired flight Ring, reboot the device and check for updates. For current Windows 10 Mobile builds, Windows Insider setup options have been migrated into Settings.

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Under Choose Your Level, select between the following rings: Fast, Slow or Release Preview. Find out more about rings. Below is a set of quick references for key information you may find useful as you participate in the program. This information will also be helpful when submitting feedback for build issues or feature suggestions, as well as reaching out for assistance.

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Validate your device is up-to-date. Builds are more frequently released to the Fast Ring than to Slow or Release Preview Rings.This will be 201 upon successful creation of the deepnet and 200 afterwards. Make sure that you check the code that comes with the status attribute to make sure that the deepnet creation has been completed without errors.

This is the date and time in which the deepnet was created with microsecond precision. True when the deepnet has been created in the development mode. The list of fields's ids that were excluded to build the models of the deepnet. Provides a measure of how important an input field is relative to the others to predict the objective field. Each field is normalized to take values between zero and one. The list of input fields' ids used to build the models of the deepnet. Specifies the id of the field that the deepnet predicts.

In a future version, you will be able to share deepnets with other co-workers or, if desired, make them publicly available.

This is the date and time in which the deepnet was updated with microsecond precision. A number between 0 and 1 specifying the rate at which to drop weights during training to control overfitting. A dictionary with an entry per field in the dataset used to build the deepnet. Whether alternate layers should learn a representation of the residuals for a given layer rather than the layer itself or not.

Complete information of the network. The key is the name of the algorithm used. Whether to learn a tree-based representation of the data as engineered features along with the raw features, essentially by learning trees over slices of the input space and a small amount of the training data.

Each layer is a map, and its structure will vary depending on the structure of the layers. This includes per-node class names for classification problems and distribution information of the objective for regression problems.

A list of maps, each one of which is a preprocessor, specifying one input feature to the network.

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This layer may comprise binary encoding, normalization, and feature selection, as there may be less preprocessors than features in the original data. A status code that reflects the status of the deepnet creation. Number of milliseconds that BigML took to process the deepnet.

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Example: 1 combiner optional Specifies the method that should be used to combine predictions in a non-boosted ensemble. For classification ensembles, the combination is made by majority vote.

The options are: 0: plurality weights each model's prediction as one vote. You can set up both using the threshold argument.

the simple layer potential for the biharmonic equation in n variables

If there are less than k models voting class, the most frequent of the remaining categories is chosen, as in a plurality combination after removing the models that were voting for class. The confidence of the prediction is computed as that of a plurality vote, excluding votes for the majority class when it's not selected.

For regression ensembles, the predicted values are averaged.


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