1. The document studies discrete breathers in a periodic chain of 5 atoms coupled by quadratic-quartic springs. It uses discrete symmetries to simplify the analysis and visualize the phase space.
2. It finds that unlike even atom chains, odd atom chains have no energy threshold for breathers due to degenerate band edge modes. It observes long-lived "hopping breathers" that move chaotically in the separatrix region dividing pinned and moving states.
3. It applies linear stability analysis to measure quasi-phonon frequencies around breathers and map the stable and unstable manifolds of unstable breathers. This allows systematically launching moving or pinned breathers by perturbing stable or unstable breathers.
A model for non-circular orbits derived from a two-step linearisation of the ...Premier Publishers
In the Solar System most orbits are circular, but there are some exceptions. The paper addresses results from a two-step linearisation of the Kepler laws, to model non-circular orbits, at Newtonian gravity and other interactions with adjacent bodies. The orbit will then be characterised by a generalised eccentricity and a secondary frequency denoted L-frequency, ωL (and considered proportional to the angular velocity). The path will be that of a circle, superimposed by small vibrations with the L-frequency. Hereby, the amplitude corresponds to an eccentricity, such that the radius varies, with time. When the ratio between the L-frequency and angular velocity is a non-integer, ‘perihelion’ moves. Bounds are derived and resulting orbits are generated and visualized.
For the integer ratio 2, results are compared with an ellipsoidal, and a tidal wave. For a non-integer ratio, the orbit is related to data for Mercury. Methods for detecting and measuring the secondary frequency are discussed, in terms of transfer orbits in Spaceflight dynamics.
Classical Mechanics of a Three Spin ClusterPaul Houle
A cluster of three spins coupled by single-axis anisotropic exchange exhibits classical behaviors ranging from regular motion at low and high energies, to chaotic motion at intermediate energies. A change of variable, taking advantage of the conserved z-angular momentum, combined with a 3-d graphical presentation (described in the Appendix), produce Poincare sections that manifest all symmetries of the system and clearly illustrate the transition to chaos as energy is increased.
The three-spin system has four families of periodic orbits. Linearization around stationary points predicts orbit periods in the low energy (antiferromagnetic) and high energy (ferromagnetic) limits and also determines the stability properties of certain orbits at a special intermediate energy. The energy surface undergoes interesting changes of topology as energy is varied. We describe the similiarities of our three spin system with the Anisotropic Kepler Problem and the Henon-Heiles Hamiltonian. An appendix discusses numerical integration techniques for spin systems.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
A model for non-circular orbits derived from a two-step linearisation of the ...Premier Publishers
In the Solar System most orbits are circular, but there are some exceptions. The paper addresses results from a two-step linearisation of the Kepler laws, to model non-circular orbits, at Newtonian gravity and other interactions with adjacent bodies. The orbit will then be characterised by a generalised eccentricity and a secondary frequency denoted L-frequency, ωL (and considered proportional to the angular velocity). The path will be that of a circle, superimposed by small vibrations with the L-frequency. Hereby, the amplitude corresponds to an eccentricity, such that the radius varies, with time. When the ratio between the L-frequency and angular velocity is a non-integer, ‘perihelion’ moves. Bounds are derived and resulting orbits are generated and visualized.
For the integer ratio 2, results are compared with an ellipsoidal, and a tidal wave. For a non-integer ratio, the orbit is related to data for Mercury. Methods for detecting and measuring the secondary frequency are discussed, in terms of transfer orbits in Spaceflight dynamics.
Classical Mechanics of a Three Spin ClusterPaul Houle
A cluster of three spins coupled by single-axis anisotropic exchange exhibits classical behaviors ranging from regular motion at low and high energies, to chaotic motion at intermediate energies. A change of variable, taking advantage of the conserved z-angular momentum, combined with a 3-d graphical presentation (described in the Appendix), produce Poincare sections that manifest all symmetries of the system and clearly illustrate the transition to chaos as energy is increased.
The three-spin system has four families of periodic orbits. Linearization around stationary points predicts orbit periods in the low energy (antiferromagnetic) and high energy (ferromagnetic) limits and also determines the stability properties of certain orbits at a special intermediate energy. The energy surface undergoes interesting changes of topology as energy is varied. We describe the similiarities of our three spin system with the Anisotropic Kepler Problem and the Henon-Heiles Hamiltonian. An appendix discusses numerical integration techniques for spin systems.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
A brief and easy concept of Simple harmonic oscillator. How we can get simple harmonic motion equation from Lagrange's equation of motion. How can we obtain this from Lagrange's equation of motion.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
ABOUT NONLINEAR CLASSIC FIELD THEORY OF CONNECTED CHARGES ijrap
On the basis of an exact solution for the field of a charge in a uniformly accelerated noninertial frame of
reference (NFR) and formulated "Equivalent Situation Postulate" the nonlinear electrostatic theory of
bound charges has been constructed. Proposed method is outside of the flat space-time, however the
curvature is not directly connected with the Einstein gravitational theory. The method proposed eliminates
divergence of the proper energy and makes classical electrodynamics consistent at any sufficiently small
distances.
Semiclassical mechanics of a non-integrable spin clusterPaul Houle
We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
A brief and easy concept of Simple harmonic oscillator. How we can get simple harmonic motion equation from Lagrange's equation of motion. How can we obtain this from Lagrange's equation of motion.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
ABOUT NONLINEAR CLASSIC FIELD THEORY OF CONNECTED CHARGES ijrap
On the basis of an exact solution for the field of a charge in a uniformly accelerated noninertial frame of
reference (NFR) and formulated "Equivalent Situation Postulate" the nonlinear electrostatic theory of
bound charges has been constructed. Proposed method is outside of the flat space-time, however the
curvature is not directly connected with the Einstein gravitational theory. The method proposed eliminates
divergence of the proper energy and makes classical electrodynamics consistent at any sufficiently small
distances.
Semiclassical mechanics of a non-integrable spin clusterPaul Houle
We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
About Nonlinear Classic Field Theory of Connected Chargesijrap
On the basis of an exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) and formulated "Equivalent Situation Postulate" the nonlinear electrostatic theory of
bound charges has been constructed. Proposed method is outside of the flat space-time, however the curvature is not directly connected with the Einstein gravitational theory. The method proposed eliminates
divergence of the proper energy and makes classical electrodynamics consistent at any sufficiently small
distances.
Schrodinger wave equation and its application
a very good animated presentation.
Bs level.
semester 6th.
how to make a very good appreciable presentation.
The Modified Theory of Central-Force MotionIOSR Journals
Everybody is in the state of constant vibration, since vibration is the cause of the entire universe.
Consequent upon this, a body under the influence of attractive force that is central in character may also vibrate
up and down about its own equilibrium axis as it undergoes a central-force motion. The up and down vertical
oscillation would cause the body to have another independent generalized coordinates in addition to the one of
rotational coordinates in the elliptical plane. In this work, we examine the mechanics of a central-force motion
when the effect of vertical oscillation is added. The differential orbit equation of the path taken by the body
varies maximally from those of the usual central- force field. The path velocity of the body converges to the
critical speed in the absence of the tangential oscillating phase.
The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data
ABSTRACT : In this paper, the simulation of a double pendulum with numerical solutions are discussed. The double pendulums are arranged in such a way that in the static equilibrium, one of the pendulum takes the vertical position, while the second pendulum is in a horizontal position and rests on the pad. Characteristic positions and angular velocities of both pendulums, as well as their energies at each instant of time are presented. Obtained results proved to be in accordance with the motion of the real physical system. The differentiation of the double pendulum result in four first order equations mapping the movement of the system.
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
Chatbots are growing in popularity as developers face the
limitations of the mobile app. User interfaces that simulate a human
conversation, the history of chatbots goes back to the late 18th
century. I'll take you on a tour of that history with an eye on finding
insights on what is possible today and in the near future with chatbots.
Issues Covered: Amazon Alexa, Facebook Messenger Chatbots, Alan
Turing, and much more.
Estimating the Software Product Value during the Development ProcessPaul Houle
Nowadays software companies are facing a fierce competition
to deliver better products but offering a higher value to the customer.
In this context, software product value has becoming a major concern
in software industry, leading for improving the knowledge and better
understanding about how to estimate the software value in early development
phases. Other way, software companies encounter problems such
as releasing products that were developed with high expectations, but
they gradually fall into the category of a mediocre product when they
are released to the market. These high expectations are tightly related
to the expected and offered software value to the customer. This paper
presents an approach for estimating the software product value, focusing
on the development phases. We propose a value indicators approach to
quantify the real value of the development products. The aim is early
identifying potential deviations in the real software value, by comparing
the estimated versus the expected. We present an internal validation
to show the feasibility of this approach to produce benefits in industry
projects.
Universal Standards for LEI and other Corporate Reference Data: Enabling risk...Paul Houle
Individual Records are supposed be updated yearly, but more than 25% of records have lapsed
LEI records must be updated sooner in response to corporate actions if the GLEIS is to be useful as golden copy reference data inside financial institutions
Needed: real-time, streaming analytics to monitor SIFI, trading and the buildup of systemic risk
LOUs publish records daily, which are concatenated by the LOUS: however, the data on organization types (Corporation, Fund, Trust, etc.), Geographic Regions, Business Registry Numbers, Hierarchy and other fields are often missing or inconsistently represented
Implementing Reference Dataand Corporate Actions in a Blockchain
Fixing a leaky bucket; Observations on the Global LEI SystemPaul Houle
We apply bitemporal analysis to more than 500 daily data files supplied by the Global Legal Entity Identifier Foundation to show that churn dominates the dynamics of growth, such that the number of paid up records in full standing has been flat over the last year. Our analysis reveals occasional daily glitches in the past that affected thousands of records. These appear to be in better control now, but a high lapse rate is the primary challenge to the Global LEI System right now
Although animals do not use language, they are capable of many of the same kinds of cognition as us; much of our experience is at a non-verbal level.
Semantics is the bridge between surface forms used in language and what we do and experience.
Language understanding depends on world knowledge (i.e. “the pig is in the pen” vs. “the ink is in the pen”)
We might not be ready for executives to specify policies themselves, but we can make the process from specification to behavior more automated, linked to precise vocabulary, and more traceable.
Advances such as SVBR and an English serialization for ISO Common Logic means that executives and line workers can understand why the system does certain things, or verify that policies and regulations are implemented
The Ontology2 platform squares the circle between big data, low latency, and semantics by combining expressive reasoning, information retrieval and machine learning with Hadoop, Apache Spark and Solid State Drive backed cloud .
Types in Freebase typically mean that something plays a role. For instance, superman is a :film.film_subject because he the subject of a film. He is an :amusement_parks.ride_theme because amusement parks have been made about him. There's nothing contradictory about this, at least to first order, because these types don't fit into a hierarchy.
Today's Enterprise Search products have effective answers for content ingestion and and query performance.
Any product that is successful at all has an answer for content ingestion. It's a complex problem because you need to interact with many kinds of system, but it's a solved problem: a vendor who hasn't solved this problem would not be successful at all.
This graph compares two importance scores for DBpedia concepts.
x-axis (left) is a usage-based importance score (based on which pages people view) and y-axis (up) is the PageRank score published by ath representing the strength of links to a concept. Correlation coefficients via kendal, spearman and pearson are in the 0.35-0.5 range.
Be warned that this system does not have a sense of "respectability" so you be offended by many of its opinions and we apologize for it.
Extension methods, nulls, namespaces and precedence in c#Paul Houle
Extension methods are the most controversial feature that Microsoft has introduced in
C# 3.0. Introduced to support the LINQ query framework, extension methods make
it possible to define new methods for existing classes.
Although extension methods can greatly simplify code that uses them, many are
concerned that they could transform C# into something that programmers find
unrecognizable, or that C#’s namespace mechanisms are inadequate for managing
large systems that use extension methods. Adoption of the LINQ framework,
however, means that extension methods are here to stay, and that .net
programmers need to understand how to use them effectively, and, in particular,
how extension methods are different from regular methods.
This article discusses three ways in which extension methods differ from regular
methods:
1. Extension methods can be called on null objects without throwing an exception
2. Extension methods cannot be called inside of a subclass
Dropping unique constraints in sql serverPaul Houle
I got started with relational databases with mysql, so I’m in the habit of making
database changes with SQL scripts, rather than using a GUI. Microsoft SQL Server
requires that we specify the name of a unique constraint when we want to drop it. If
you’re thinking ahead, you can specify a name when you create the constraint; if
you don’t, SQL Server will make up an unpredictable name, so you can’t write a
simple script to drop the constraint.
This is a story of two types: GenericType and SpecificType, where GenericType is a
superclass of SpecificType. There are two types of explicit cast in C#:
The Prefix cast:
[01] GenericType g=...;
[02] SpecificType t=(SpecificType) g;
The as cast:
[03] GenericType g=...;
[04] SpecificType t=g as SpecificType;
Most programmers have a habit of using one or the other — this isn’t usually a
conscious decision, but more of a function of which form a programmer saw first. I,
for instance, programmed in Java before I learned C#, so I was already in the prefix
cast habit. People with a Visual Basic background often do the opposite. There are
real differences between the two casting operators
I'm an expert on building commerical large scale systems based on Linked Data sources such as Freebase and DBpedia. I'm the creator of :BaseKB, which was the first correct conversion of Freebase to RDF and of Infovore, the open source
I do consulting on the following areas:
* Data processing with Hadoop and the design and construction of systems using Amazon Web Services
* Architecture and construction of systems that consume and produce Linked Data
* Construction and evaluation of intelligent systems that make subjective decisions (text search, text classification, machine learning, etc.)
I'm not at all interested in doing maintenance work on other people's code, but I am interested in helping you align your process, structure, and tools to speed up your development cycle, improve your products, and prevent developer burnout. I am not free to relocate at this time, but I collaborate all of the time with workers around the world and I can travel to your location, understand your needs and transfer skills to your workforce.
Keeping track of state in asynchronous callbacksPaul Houle
There’s a lot of confusion about how asynchronous communication works in RIA’s
such as Silverlight, GWT and Javascript. When I start talking about the problems of
concurrency control, many people tell me that there aren’t any concurrency problems
since everything runs in a single thread. [1]
It’s important to understand the basics of what is going on when you’re writing
asynchronous code, so I’ve put together a simple example to show how execution
works in RIA’s and how race conditions are possible. This example applies to
Javascript, Silverlight, GWT and Flex, as well as a number of other environments
based on Javascript. This example doesn’t represent best practices, but rather what
can happen when you’re not using a proactive strategy that eliminates concurrency problems
Mat Byrne recently posted source code for a dynamic domain object in PHP which
takes advantage of the dynamic nature of PHP. It’s a good example of how
programmers can take advantage of the unique characteristics of a programming
language.
Statically typed languages such as C# and Java have some advantages: they run
faster and IDE’s can understand the code enough to save typing (with your fingers),
help you refactor your code, and help you fix errors. Although there’s a lot of things I
like symfony, it feels like a Java framework that’s invaded the PHP world. Eclipse
would help you deal with the endless getters and setters and domain object methods
with 40-character names in Java, Eclipse.
The limits of polymorphism are a serious weakness of today’s statically typed
languages. C# and Java apps that I work with are filled with if-then-else or case
ladders when they need to initialize a dynamically chosen instance of one of a set of
classes that subclass a particular base class or that implement a particular interface.
Sure, you can make a HashMap or Dictionary that’s filled with Factory objects, but
any answer for that is cumbersome. I
articles on asynchronous communications with a focus on Javascript.
Minimizing Code Paths In Asynchronous Code, a recent post of his, is about a lesson
that I learned the hard way with GWT that applies to all RIA systems that use
asynchronous calls. His example is the same case I encountered, where a function
might return a value from a cache or might query the server to get the value: an
obvious way to do this in psuedocode is:
function getData(...arguments...,callback) {
if (... data in cache...) {
callback(...cached data...);
}
cacheCallback=anonymousFunction(...return value...) {
... store value in cache...
callback(...cached data...);
}
getDataFromServer(...arguments...,cacheCallback)
}
At first glance this code looks innocuous, but there’s a major difference between
what happens in the cached and uncached case. In the cached case, the callback()
function gets called before getData() returns — in the uncached case, the opposite
happens. What happens in this function has a global impact on the execution of the
program, opening up two code paths that complicate concurrency control and
introduce bugs that can be frustrating to debug.
This function can be made more reliable if it schedules callback() to run after the
thread it is running in completes. In Javascript, this can be done with setTimeout().
In Silverlight use System.Windows.Threading.Dispatcher. to schedule the callback
What do you do when you’ve caught an exception?Paul Houle
This article is a follow up to “Don’t Catch Exceptions“, which advocates that
exceptions should (in general) be passed up to a “unit of work”, that is, a fairly
coarse-grained activity which can reasonably be failed, retried or ignored. A unit of
work could be:
an entire program, for a command-line script,
a single web request in a web application,
the delivery of an e-mail message
the handling of a single input record in a batch loading application,
rendering a single frame in a media player or a video game, or
an event handler in a GUI program
The code around the unit of work may look something like
[01] try {
[02] DoUnitOfWork()
[03] } catch(Exception e) {
[04] ... examine exception and decide what to do ...
[05] }
For the most part, the code inside DoUnitOfWork() and the functions it calls tries to
throw exceptions upward rather than catch them.
To handle errors correctly, you need to answer a few questions, such as
Was this error caused by a corrupted application state?
Did this error cause the application state to be corrupted?
Was this error caused by invalid input?
What do we tell the user, the developers and the system administrator?
Could this operation succeed if it was retried?
Is there something else we could do?
Although it’s good to depend on existing exception
Extension methods, nulls, namespaces and precedence in c#Paul Houle
Extension methods are the most controversial feature that Microsoft has introduced in C# 3.0. Introduced to support the LINQ query framework, extension methods make it possible to define new methods for existing classes.
Although extension methods can greatly simplify code that uses them, many are concerned that they could transform C# into something that programmers find unrecognizable, or that C#’s namespace mechanisms are inadequate for managing large systems that use extension methods. Adoption of the LINQ framework, however, means that extension methods are here to stay, and that .net programmers need to understand how to use them effectively, and, in particular, how extension methods are different from regular methods.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
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The phase plane of moving discrete breathers
1. arXiv:cond-mat/9704118v114Apr1997
PREPRINT February 1, 2008
The phase plane of moving discrete breathers
Paul A. Houle
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853-2501
Abstract
We study anharmonic localization in a periodic five atom chain with
quadratic-quartic spring potential. We use discrete symmetries to eliminate
the degeneracies of the harmonic chain and easily find periodic orbits. We
apply linear stability analysis to measure the frequency of phonon-like dis-
turbances in the presence of breathers and to analyze the instabilities of
breathers. We visualize the phase plane of breather motion directly and de-
velop a technique for exciting pinned and moving breathers. We observe
long-lived breathers that move chaotically and a global transition to chaos
that prevents forming moving breathers at high energies.
PACS numbers: 03.20.+i,63.20.Ry,63.20.Ls
Typeset using REVTEX
1
2. A body of theoretical work has appeared in the past decade on intrinsic localized modes
in perfect anharmonic crystals. [1] Although the existence of breather periodic orbits with
localized energy is established [2], less is known about the rest of the phase space. In this
paper, we use a periodic chain of five atoms coupled by a quadratic-quartic springs as a model
for larger chains and as a testbed for techniques which can be applied to other systems. We
use discrete reflection symmetries to find submanifolds on which finding breather solutions
is simplified and on which breather solutions can be continued to the phonon limit. We
introduce coordinates for visualizing breather motion, exhibiting the movability separatrix
introduced in [3], and detecting chaos in the separatrix region which leads to long-lived
breathers that move erratically. We also apply linear stability analysis to investigate phonon-
like excitations in the presence of a breather and to map the stable and unstable manifolds
of an unstable breather, developing a technique to systematically launch moving and pinned
breathers complementary to existing methods. [5].
Introducing our system, the Hamiltonian is
H =
N
i=1
M
p2
i
2
+
N
i=1
U(qi − qi−1), N = 5 (1)
U(x) =
K2
2
x2
+
K4
4
x4
. (2)
under condition that K4 > 0. By scaling qi and pi we set M = K2 = K4 = 1 without
loss of generality. The system has four nontrivial degrees of freedom since center of mass
momentum is conserved. To get numerical results we integrate the equations of motion for
(1) by fifth-order Runge-Kutta with a fixed step size of 10−3
. [6] Because a high amplitude
breather is localized on a few atoms, it is reasonable that our small model captures much
of the physics of larger chains. To check this we transplanted both even and odd breather
solutions of the N = 5 chain at energy E = 3 onto a N = 20 chain with all other atoms
initially at rest with zero displacement; we found the breather remained localized for over
one thousand breather oscillations without obvious loss of amplitude.
We take advantage of discrete symmetries to explore a subspace of the complete phase
2
3. space of the chain; because breather periodic orbits lie on these subspaces, we can use
symmetry to find breathers and to follow breather solutions all the way to the E = 0 phonon
limit. The Hamiltonian (1) respects two kinds of reflection symmetry which we refer to as
even and odd symmetry after the even-parity and odd-parity breathers in prior literature.
[14] The displacements and momenta of an even breather have even parity with respect to
reflections around a bond. (the pattern of displacements is roughly q = (−1
6
, 1, −1, 1
6
, 0)
for a even breather on the bond between atoms 2 and 3). We refer to this property as
even symmetry and the submanifold of the phase space with even symmetry as the even
manifold. The odd-parity periodic orbit has odd symmetry, odd parity with respect to
reflections around an atom. (displacements are roughly q = (0, −1
2
, 1, −1
2
, 0) for an odd
breather centered on atom 3) The submanifold of the chain with odd symmetry is the odd
manifold. Even and odd symmetry are respected by the dynamics; if the system starts
in the even or odd submanifold it remains there for all time. Even and odd manifolds,
of course, exist for each site but as the chain is translationally invariant the dynamics are
identical at all sites. Even and odd symmetry can be used to simplify any sized chain — the
use of symmetry is particularly advantageous for the N = 5 chain since the even and odd
submanifolds are reduced to two degree of freedom systems which are simple to understand
and visualize.
Unlike chains with an even number of atoms [7] [8] there is no energy threshold for
breathers in a chain with an odd number of atoms. As the energy E → 0 we expect the
anharmonic chain to be approximated by a harmonic chain for short times. For N=5, the
harmonic chain has two degenerate pairs of normal modes with wavenumbers kn = nπ
5
and
frequencies ω±1 = 2 sin π
5
and ω±2 = 2 sin 2π
5
. The modes with the highest k are band-edge
modes. In general, chains with an even number of atoms have a single band edge mode
with wavenumber π and chains with an odd number of atoms have two degenerate band
edge modes. Since any linear combination of two phonons with the same frequency is a
periodic orbit of a harmonic chain, each degenerate pair of phonons is associated with a two
parameter family of periodic orbits. This degenerate situation is structurally unstable and is
3
4. shattered when the slightest amount of K4 is turned on. Since only one linear combination of
phonons intersects each submanifold, we can remove the degeneracy by restricting ourselves
to an even or odd manifold on which a single parameter family of periodic orbits survives
in the anharmonic system. Specifically, a band-edge phonon with even or odd symmetry
deforms continuously into an even or odd breather as energy increases. No bifurcation
occurs, thus there is no energy threshold for the formation of a breather in an N odd
chain. The situation is different from that in N even chains for which there exists a single
band-edge mode possessing both even and odd symmetry which undergoes a symmetry-
breaking tangent bifurcation at an energy proportional to N−1
into two different periodic
orbits corresponding to both even and odd breathers. [7] [8]
Poinc´are sections are effective for visualizing dynamics on the submanifolds and provide
a method of finding breather solutions. Although restriction to submanifolds should simplify
the search for breathers for a system of any size, it is very advantageous for N = 5 where the
problem is reduced to a one dimensional root search. Periodic orbits manifest as fixed points
of the Poinc´are map on the surface of section q3 = 0, ˙q3 > 0. We plot surfaces of section
by integrating the equation of motion until the trajectory crosses the surface of section —
at this point we use Newton-Raphson to solve for the duration of a Runge-Kutta step that
lands on the surface of section. Fixed points corresponding to breather periodic orbits lie on
the q1 = 0 line and can be found by a simple 1-d root search by the Brent algorithm. [9] Both
the even and odd manifolds can be visualized by plotting (q1, p1); since the submanifolds
are two-dimensional, the result is a complete description of the dynamics on a submanifold.
Fig. 1 is an example. Chaos is prevalent in odd manifold sections above E = 1; we have not
observed obvious chaos in the even manifold in the range 0 < E < 300 that we’ve studied.
We use surfaces of section with a different method of projection to directly visualize the
movability separatrix introduced in [3] in a manner that should be useful for characterizing
moving and pinned modes in other breather systems. The phase plane of breather motion
at E = 10 is seen in Fig. 2. The location of the breather is given by the angle θ = Arg h
where
4
5. h =
N
i=1
p2
i
2
ei2π
N
n
+
N
i
U(qi − qi−1)ei2π
N
(n+ 1
2
)
, (3)
with N=5. (3) is a complex weighted average of the kinetic and potential energy on each
atom and bond that takes in account the circular nature of the chain, a strong influence on
small chains. [10] We construct a variable conjugate to θ by treating δθ = θn − θn−1. as the
velocity of the breather. The q3 = 0 trigger works well when a breather is localized in the
range 1 < θ < 5. [11] Unlike Fig. 1, Fig. 2 is a projection from a high-dimensional space to
the plane and is not a complete picture of the dynamics. The curves in Fig. 2 is consistent
with the hypothesis [3] [4] that two sets of action-angle variables exist approximately for
breather states; one set connected with the breather’s spatial position and velocity and a
set of “internal” degree of freedoms associated with breathing. As occurs for the pendulum,
the position-velocity conserved surfaces change topology at the separatrix dividing pinned
and moving states. Even the slightest degree of nonintegrability breaks conserved surfaces
in the separatrix creating a layer of chaos. [12] We refer to the chaos observed in this sepa-
ratrix as hopping chaos because trajectories within the separatrix region move erratically in
space while remaining localized for thousands of oscillations or more as observed in Fig. 3.
Hopping breathers have been observed to decay, so it is clear that the hopping chaos region
of phase space is connected to delocalized chaotic regions; however, the region of hopping
chaos appears to be sufficiently hemmed in by KAM tori that hopping chaos is a distinct
intermediate-term behavior. The region of hopping chaos enlarges as energy increases; near
E = 20 a global transition to chaos in the phase plane of Fig 2 appears to occur and it
becomes impossible to create moving modes; only the islands of near integrability corre-
sponding to pinning on a bond remain. Hopping chaos is probably less robust in longer
chains since longer chains have more degrees of freedom for resonances to occur with and
for energy to be radiated into.
Numerical linear stability analysis gives a local picture of the phase space around a
periodic orbit complementary to the more global views of previous sections. With stability
analysis we examine phonon-like excitations in the presence of breathers and analyze the
5
6. instabilities of breathers. Let us write the state of the system as a phase space vector
x = (q, p); let x0 be a point on a periodic orbit with period T. We make an infinitesimal
change δx in the initial conditions, launching the system at time t = 0 in state x = x0 + δx.
When we observe the system at time t = T the system is in state xT = x0 + δxT . To linear
order in δx
δxT = Sδx0 + O(δx2
0) (4)
where S is the stability matrix.
With an accurately known periodic orbit we can determine S numerically by making
copies of the system and perturbing them successively in each position and momentum
coordinate and then evolving each system for time T. [13] To interpret the stability matrix,
we first find eigenvalues and eigenvectors with EISPACK. [9] For a Hamiltonian system S
is a symplectic matrix with certain constraints on the eigenvalues and eigenvectors. [12]
In our application, eigenvalues values come in three kinds of pairs; elliptic pairs λ = e±iφ
indicating phonon-like excitations in the presence of a breather, hyperbolic pairs λ1 = λ−1
2
with λ1 real indicating instabilities and parabolic pairs λ1 = λ2 = 1 arising from conserved
quantities. In our application two parabolic pairs arise due to conserved quantities; one
pair due to conservation of momentum and another due to conservation of energy — these
uninteresting pairs are removed by automated inspection of eigenvectors.
Stability analysis confirms that the even breather known to be stable in long chains [14] is
linearly stable in the five atom chain; no hyperbolic eigenvalues appear in the energy range
from E = 0 – 200. If a stable breather is infinitesimally perturbed, one excites phonon-
like disturbances that we call quasi-phonons; by investigating quasi-phonons one can study
the interaction between a breather and phonons, crucial for understanding quantum and
thermal fluctuations around breathers. [15] We determine the frequencies of quasi-phonons
from eigenvalues of the stability matrix; Fig 4 plots quasi-phonon frequencies as a function of
breather energy. To test the accuracy of our technique, we excited quasi-phonons by making
a small change in the E = 3 and E = 50 breather solutions; quasi-phonon frequencies
6
7. appeared as peaks in the power spectrum determined by running the system until t = 3000
and taking the FFT of one atom’s position as a function of time. The two methods agree to
within one part in 10−4
, the bin size of the power spectrum. Quasi-phonon frequencies vary
smoothly with breather energy and converge on the true phonon frequencies as the energy of
the breather goes to zero. Therefore we label quasi-phonons by the symmetry they uphold
and the wavenumber kn of the phonon they become in the E → 0 limit, a scheme that
should remain applicable for quasi-phonons in larger chains and higher dimensions. The
n = 2 quasi-phonon is tangent to the phase plane of breather motion; a small excitation of
the n = 2 quasi-phonon causes the breather to rock around one bond while a large excitation
causes the breather to break free and move as has been observed in a φ4
lattice. [5]
Perturbation of a stable breather has been used to create moving breathers in a φ4
lattice [5]; we have found an alternate method of creating pinned and gliding breathers by
perturbing an unstable breather. As is known for large chains, [14] the odd breather is
linearly unstable for all energies; the linear instability does not cause the breather to decay
but instead causes the breather to move. The eigenvectors of S with eigenvalues less than
and greater than one point respectively into the stable and unstable manifolds and define
a plane tangent to the phase plane of Fig. 2. As the energy of the odd breather goes to
zero, the unstable mode eigenvectors converge on the even band-edge phonon. The tangent
plane is divided into four quadrants by the stable and unstable manifolds; distinct regular
behaviors are observed for perturbations directed into each quadrant as illustrated by the
drawn-in separatrix in Figure 2 — the unstable manifolds of an odd breather at one site feed
into the stable manifolds of odd breathers at neighboring sites. By choosing a quadrant we
can launch a breather that travels either to the left or to right or that remains pinned while
rocking slightly to the left or right of the odd breather location. To get reliable results it is
necessary to add a sufficiently large perturbation so as to clear the region of hopping chaos
in the separatrix region.
In summary, we have found the N = 5 chain exhibits much of the phenomenology of larger
chains and can be used as both a model of localization and a testing ground for techniques.
7
8. We have applied numerical stability analysis to to measure quasi-phonon frequencies in the
presence of a breather and to design perturbations that create either moving or pinned
modes starting from either a stable or an unstable breather. Chaos exists in the movability
separatrix and becomes increasingly prevalent as the energy increases; a global transition
to chaos near E = 20 makes it impossible to launch moving breathers. With appropriate
coordinates we have been able to directly visualize the phase plane of breather motion.
I would like to thank C. Henley for suggesting equation (3) and other useful discussions
as well as Rongji Lai, S. A. Kiselev and A. J. Sievers. This work was supported by by NSF
Grant DMR-9612304.
8
9. FIGURES
−2.3 −0.3 1.7
q1
−12.0
−2.0
8.0
p1
FIG. 1. A Poinc´are section on the odd submanifold at E = 230; the phase space is dominated by
chaotic trajectories, although two large islands of regularity are visible. The upper island consists
of an unstable breather and phonon-like disturbances around it while the lower island is due to a
high-amplitude standing wave associated with the n = ±1 phonons; resonant islands in the upper
half of the plot involve phase locking between the breather and quasi-phonons
9
10. 1.0 2.0 3.0 4.0 5.0
theta
−0.4
−0.2
0.0
0.2
0.4
deltatheta
I
III
IIIV
FIG. 2. A Poinc´are section using the q3 = 0 trigger and the variable θ illustrating the pendu-
lum-like phase plane of moving breathers. The dotted line is drawn in and illustrates the separatrix;
circles mark stable (even) breather solutions and crosses mark unstable (odd) breather solutions.
Roman numerals indicate four regions in phase space divided by stable and unstable manifolds in
which distinct regular behaviors are observed. In regions I and III the breather moves to the left
and right respectively while it is pinned at either side of site three in regions II and IV.
10
11. 0.0 500.0 1000.0 1500.0 2000.0
time
−10.0
−5.0
0.0
5.0
10.0
displacement
FIG. 3. Hopping chaos observed at E = 50 for a small perturbation in region III. Although
energy is localized throughout the duration of the simulation, the breather moves erratically. The
atoms are visually separated by adding constants to the displacements; the chains is periodic so
the bottom atom is adjacent to the top atom.
11
12. 0.0 50.0 100.0 150.0 200.0
breather energy
0.0
2.0
4.0
6.0
8.0
angularfrequency
even breather
band edge odd quasi−phonon (n=2)
even n=1 quasi−phonon
odd n=1 quasi−phonon
FIG. 4. Breather and quasi-phonon frequencies from the stability matrix for even breathers on
a 5-atom quadratic-quartic chain. The wavenumber of a quasi-phonon is k = ±2π
5 n
12
13. REFERENCES
[1] S. Flach, C.R. Willis Physics Reports in press (1997)
[2] R.S. MacKay, S. Aubry Nonlinearity 7 1623 (1994)
[3] S. Flach, C.R. Willis Phys. Rev. Lett. 72 1777 (1994)
[4] S. Flach, C.R. Willis, E. Olbrich Phys. Rev. E 49 836 (1994)
[5] Ding Chen, S. Aubry, G. P. Tsironis Phys. Rev. Lett. 77 4776 (1996)
[6] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P.Flannery Numerical Recipes in C,
2nd edition (Cambridge University Press, New York 1992)
[7] S. Flach Physica D 91 223 (1996)
[8] K.W. Sandusky, J.B. Page Phys. Rev. B 50 866 (1994)
[9] http://www.netlib.org/
[10] A similar variable applicable only for large chains is used in [3]
[11] Triggering fails near θ = 0; perfect triggering is difficult since it is impossible to assign
alternating signs to five atoms in a ring.
[12] A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics, 2nd edition
(Springer-Verlag, New York 1992)
[13] Our increment was 10−6
, the stability matrix was insensitive to changes in the increment.
[14] K.W. Sandusky, J.B. Page, K.E. Schmidt Phys. Rev. B46 6161 (1992)
[15] S. Aubry Physica D in press (1997)
13