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ψ ( r ) = max [ 0 , min [ min ( 1 , d 0 + d 1 r ] , 1 c c r ] ]

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In many of the aforementioned advection schemes the behavior in multiple dimensions is not necessarily as good as the one dimensional behavior. For instance, a shape preserving monotonic scheme in one dimension can have severe shape distortion in two dimensions if the two components of horizontal fluxes are treated independently. There is a large body of literature on the subject dealing with this problem and among the fixes are operator and flux splitting methods, corner flux methods, and more. We have adopted a variant on the standard splitting methods that allows the flux calculations to be implemented as if in one dimension:

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τ n + 1 / 3 = τ n Δ t ( 1 Δ x δ i F x ( τ n ) τ n 1 Δ x δ i u ) τ n + 2 / 3 = τ n + 1 / 3 Δ t ( 1 Δ y δ j F y ( τ n + 1 / 3 ) τ n 1 Δ y δ i v ) τ n + 3 / 3 = τ n + 2 / 3 Δ t ( 1 Δ r δ k F x ( τ n + 2 / 3 ) τ n 1 Δ r δ i w )

In order to incorporate this method into the general model algorithm, we compute the effective tendency rather than update the tracer so that other terms such as diffusion are using the n time-level and not the updated n + 3 / 3 quantities:

Walled Garden vs. API

Apps can be closed or open or anywhere in between, from managed services and self-serve to accessible/limited partnerships or RTB accessible, with each choice having data and targeting implications.

Features Platform Capabilities

Beyond texting, any app can include virtually infinite options for adding additional features and capabilities: ads, calling, chatbots, e-commerce, media sharing, gaming, GIFs, stickers, voice messages, video, and many more. When picking and choosing apps and functions, ask yourself how your message can enhance the experience for the consumer.

3rd Party Creative Integration

There are a number of 3rd party solutions that can create campaigns for publishers and marketers to scale the reach of their creative across multiple platforms. This is very true for chatbots. Knowing that there are scalable options may make it easier for you to begin exploring marketing options to meet your goals.

Mobile vs. Desktop (or Both)

While apps with messaging funcationality are generally considered to be mobile-only, that is not always the case. This could potentially impact your creative as you’ll want to ensure a great consumer experience, regardless of screen size.


Messaging Takes Place Between People, Not Between Bots. So Where Do Chatbots Fit in the Messaging Space?

Bots will allow brands to build a stronger relationship with the user while the user decides the frequency, the medium (which platform), and the context of engagement with the brand, as opposed to email that is being sent when the brand thinks is the best time.

Chatbots as a component of messaging are important and will become increasingly more so as technology evolves and bot capabilities expand.

Bots offer to publishers and brands a personal way to engage with consumers through a channel they already likely use—messaging. While much of the industry conversation about chatbots has focused on e-commerce and customer service, chatbots offer functionality to forge increasingly personal connections with consumers on multiple levels.Bots can run the gamut from “conversational” to “experiential,” leveraging other forms of interaction that consumers are accustomed to from the app world. Convincing consumers to use a chatbot within the messaging space is a win-win-win: The app gains desired stickiness, the brand benefits from enhanced communication with the user, and the consumer benefits from real-time interactions in a space where they are already active.

As a starting point for understanding chatbots on messaging platforms, IAB identified the top five chatbot capabilities most likely to be found within messaging apps:

Top 5 chatbot capabilities with messaging function apps

Personal Connection

Chat bots give brands a voice and a means of “entering the conversation” with their customers. Versus social media, chat bots on messaging apps offer more personalized 1:1 conversations and experiences between users and brands without the risk of potentially damaging public comments to deal with. Plus, with bots, all customers can feel like they are connected and communicating directly with the brand versus just a select few customers handpicked from the traditional social media forums.


Bots can facilitate new mobile experiences all in one place from viral gaming to discovery of new interests, connecting with people sharing common interests, and more. They offer a rich media interface that allows multiple media types as well. Developers are creating new rich and engaging bot experiences every day so we can expect new discovery options in the future.


Most chatbots can cut through the clutter and give consumers informed answers to questions (e.g., they do the searching for them). As AI improves, bots can get smarter and begin tailoring their responses to the individual.

Online to Offline

Chatbots can connect directly from online to offline experiences leveraging scan codes. Unlike QSR codes, scan codes bring the consumer into a chat platform that they are already familiar with and where have they can chat with a bot on the platform. This is convenient because they likely already have their information entered into the chat app (email, phone #, credit card, etc.). Messaging app scan codes are relatively frictionless and while they have huge adoption in Asia and other parts of the globe, the expectation is that they will gain more momentum in the U.S. as Americans get more comfortable transacting with their phones.


Chatbots help users get things done more efficiently on mobile devices without needing to download new apps or struggle to fill out unfamiliar web pages. Chatbots can interface with multiple systems, giving users the power to request and receive information via a common chat interface.

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In our survey with leaders in the pure-play and hybrid messaging space we asked:

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