If you just started taking Super P-Force or are thinking about using it, you should know more about it than the usual stuff you hear and read about the Generic drug. Some people say that what I'm going to tell you just happens to the minority of men but I have spoken to dozens of men who have made the same or similar experience with Super P Force… and I don't want to know how many guys actually go through the same and just don't want to talk about it.
Well, you might be asking yourself what happened and where this is going, but I feel I need to explain a bit more about Super P Force online and general things that are also important to know before making the decision of getting some help in you sexual performance by Super P Force.
So, what IS Super P Force actually?
Is Super P-Force a Generic Drug?
Super P Force is one of the most sold generic drugs on the market. Generic drugs are drugs that contain the same ingredients as the official version. The only difference is that the original version is much more expensive and has a different name. Super P-Force is the same as …. only for a lesser price. The drug companies aren't very happy about this but we guys who use stuff like Super P Force are grateful for websites where they sell Super P Force, Kamagra and Tadalista etc.
But what is it you REALLY need to know about Super P Force?
Well, let me tell you about my own experience with Super P Force. And as I mentioned before, many many other men have complained about the same issue.
After taking Super P Force for the very first time a few years ago, I was really happy to have found this wonder pill. I was very interested in this girl I knew but wasn't confident enough to approach her as I was aware of my problem in the bedroom. I didn't feel I could satisfy her and I honestly was scared she would laugh at me and tell all her girlfriends.
What I had been afraid of before using Super P Force, actually happened BECAUSE I had taken Super P Force and she told all her girlfriends of me and my super performance! I was looking for a girlfriend but as new doors opened up to me, I just couldn't resist but go for one of her girlfriends after another. The funny thing is that THEY approached ME and I didn't have to do anything… I really tried to focus on the girl I had my first Super P Force experience with, but men, when 3 hot girls try to seduce you every weekend in a club, you just go for it!
So, the negative side effect of Super P Force is simply that you won't be able to have a stable relationship when you're looking for a girlfriend and she tells everyone. And you know how most women are…. They just tell their girlfriends EVERYTHING!!
Other than this, I haven't had any side effects using Super P Force!
Browse Here for getting more information related to Enjoying the Best of Both World's.


It's Sarah Herring coming at you from Bucharest with a brand new episode of the PokerNews Podcast. She flies solo on this one (Jeff Platt is probably firing a nightly tournament somewhere in Vegas), but gets some help from 888 Poker Ambassador Ana Marquez. The two dive into a wide-ranging conversation at the 888 Poker LIVE event in Bucharest. Plus, Sarah looks at the top stories in the poker world. This week's sponsor: Natural8!
PokerNews Podcast: Who Stole Sarah's Truck?
It's another episode of the PokerNews Podcast, featuring a special recap of the PokerStars Caribbean Adventure. Jeff Platt is in the Bahamas covering the festival, and Sarah Herring chats with Platinum Pass winner Aleeyah Jadavji about an incredible experience at the PokerStars Players Championship. Plus, Jadavji explains her thought process behind leaving Poker League of Nations.


text:
Coyote Yipps
Information and stories about San Francisco coyotes: behavior & personality, coexistence & outreach, by Janet Kessler: Unveiling first-hand just how savvy, social, sentient and singular coyotes really are!
Coyote Voicings: Howls, Yips, Barks, & More
Take A Short Coyote Survey
UrbanCoyoteSquared: GALLERY
*FIRST: A Guidelines and Safety Box
Introducing My Coyote Yipps Blog
San Francisco as Habitat and Place
Contents By Topic
Responding to Recent Postings on Social Media: A Recap of Some Urban Coyote Behaviors and Some Explanations
01 Jun 2016 6 Comments
by yipps:janetkessler in coexisting with coyotes, communication, coyote "attacks", coyote "messaging" behavior, coyote behavior, Coyote encounters, coyote reactions to dogs, coyote safety, coyotes, coyotes and cars, coyotes and dogs, coyotes and human behavior, coyotes defending themselves, coyotes sighted in neighborhoods, critical distance, curiosity, dog reactions to coyotes, feeding, harassment by other animals, marking, shooing off a coyote, social media, territoriality, territoriality, video, wariness Tags: coyote behavior, coyote coexistence, coyotes playing, dogs and coyotes, habituation and coyotes, understanding coyote behavior, urban coyote behavior
This posting is a slightly revised and expanded version, with photos, of what was originally written for, and posted on, Bernalwood.com on May 27th.
coyote at dawn
We have coyotes in most of our parks here in San Francisco, and most folks I've spoken with are thrilled about it! Enjoy it and respect its wildness! At the same time, there are some people, especially pet owners, who are not so thrilled. Here is some information I've put together about coyotes, much of it based on my own observations, as a response to concerns and comments which have appeared in some of the social media recently. This is information that applies to urban coyotes everywhere, not just here in SF.
COYOTES ARE TERRITORIAL AND LIVE IN FAMILIES
coyotes in our parks
Most parks in San Francisco have one stable resident family, or a loner. Coyotes are not "pack" animals of unrelated individuals. Families "claim" territories which they "own" from which they exclude other coyotes — this is what keeps the population density down. They trek through the neighborhoods every night, during the early morning or early evening hours — and, more rarely, during the brightest hours of the day — marking their territories to keep other coyotes out and looking for hunting opportunities. Studies show that in urban areas, there is generally about one coyote per square mile — a family of 4 would require about 4 square miles. You will always be seeing the same individual coyotes in any particular area.
Although we have parks with loner coyotes, most parks have mated pairs with families. Coyotes mate for life, and both parents raise the young. Coyotes mate in January or February and produce young in April — births occur only once a year.
The number of family members fluctuates up and down continually over time. In one park, it went something like this: 2-5-3-4-2. The fluctuation is due to new pups, and then to their dispersal or deaths. There is only about a 30% survival rate of pups during their first year — disease and nutritional issues take their toll.
When it's time for youngsters to "disperse", the parents will drive them out, or they may just pick-up-and-go. This usually occurs between one and two, and sometimes three years of age, and it occurs throughout the year — there is no "dispersal season". However, the breeding adult pair will remain in the same territory over many years. Interestingly, wolves will actually kill their own kin in order to preserve their own statuses and territorial rights. I've not seen this in coyotes, but I have seen the altercations that drive coyotes out of their birth territories.
Cars are urban coyotes' chief cause of death — please drive carefully! They often trek on our traffic grid — it's often the "path of least resistance". A few days ago, in our Diamond Heights neighborhood, a car swerved right into someone's house to avoid hitting a coyote during the early morning hours.
MORE ASSERTIVE OR INSISTENT BEHAVIOR
coyote shows her anxiety and displeasure with a dog by jumping up and down
As the individuals in a family mature, some of them may go through phases of what might be called more "assertive" or "insistent" behavior, such as: following or running in the direction of a dog. During pupping season, the assertiveness is strongest, with coyotes even approaching and possibly even nipping at a dog's haunches. These are coyote "messaging" behaviors: coyotes want dogs to move on and to know the territory is taken. These behaviors don't "define" a coyote, and they don't last. Think of these as phases in a teenager's life, or in a parent's life — there's an ebb and flow to behaviors for each coyote, often based on what is going on within the coyote's individual family: Are there new pups? Is there increased sibling rivalry? Are parents having issues with the offspring, or trying to get one to disperse? I've seen no evidence to indicate that such behaviors build up towards more aggressiveness. Many of the more apparently "assertive" behaviors, both in juveniles and adults, are based solely on circumstances and happenstance encounters, so keep your distance.
trekking through the neighborhood
A substantial increase in "sightings" doesn't necessarily translate into a spike in the coyote population, though this is what many people assume. Again, increased sightings could be due to their current family dynamics which may cause individuals to wander farther afield.
Unusual weather conditions can have an effect on sightings. San Francisco has just been through a four-year drought. Drought conditions cause coyotes to hunt further afield and for longer hours. They become more visible to humans and more prone to incidents during these times when their activity overlaps with ours. It takes 8 full months for an ecosystem to recover from a drought.
Human changes to the environment, including new construction, will affect coyotes in an area. In San Francisco, coyotes may be lingering longer in neighborhoods recently, and therefore be seen more, because of the current program of thinning and eliminating dense and protective thickets in the parks, reducing coyotes' normal secure habitat. Stopping the destruction of the habitat, and compensating for the exceptional weather or drought in various ways until the ecosystem has recovered, both are steps that could be taken to reduce sightings, and possible dog/coyote encounters, and coyotes' spending the past-twilight hours in neighborhoods.
feeding coyotes is not good
Please don't feed the coyotes. Feeding breaks down the barrier that keeps coyotes wild. If they become food conditioned — which is different from "habituation" (see below) — problems could develop, including approaching people, which increases the chances for a negative incident to occur. Feeding them also encourages them to hang around yards where people don't want them.
Coyotes are opportunistic eaters, which means they can eat almost anything, but their preference in San Francisco is for gophers, squirrels and voles, which they eat whole: they need the meat, muscle, bones, fur — all of it — to nourish themselves properly. They also eat fruit, nuts, bugs, weak or juvenile raccoons, skunks, opossums, and possibly snakes. They prefer their whole foods over human-made foods, but if that human food is available, they'll try it. And they will eat the occasional cat or small dog if circumstances are right — they don't know who is a pet and who isn't. Don't create the right circumstances that could add your pet to the food chain. Please protect your pets by not allowing them to roam free and by supervising them closely when out-of-doors.
As top predators to an area, coyotes have helped rebalance the environment: they control rodents and some mesopredators, such as opossums, skunks and raccoons.
HABITUATION
a habituated coyote is not a dangerous coyote
Urban coyotes do not "fear" humans — that is an incorrect term. Rather they are "wary" of humans. This means that, although a coyote won't flee lickety-split in fear when they see a human, they nonetheless will maintain distance and not approach us. And we, in turn, need to respect them and their wildness by keeping as far away from them as we can. "Habituation" is a normal progression in urban areas — you cannot prevent it because you cannot stop coyotes from seeing humans on a daily basis — they get used to seeing us. A habituated coyote is not a dangerous animal. In fact, the term "habituation" was first used to describe bears as being more dangerous if they got used to people and lost fear of us. This assumption has been turned on its head: scientists now know that bears who are habituated tend to ignore humans, whereas bears who have never seen humans become reactive. In Africa, to make gorillas less reactive to humans, for the tourist trade, people purposefully habituate them — they become less dangerous.
Coyotes also habituate to "hazing" tactics, which is why such tactics should not be used if a coyote is way out in left field. Scaring off a coyote should be used sparingly. It should be reserved for when a coyote has come too close to you. It is a useless tactic unless the coyote is closer than 50 or so feet to you, which generally delineates its critical distance for discomfort.
Note that "habituation" is different from "food conditioning". When visibly feeding or hand-feeding a coyote, you are conditioning it to approach humans. Don't feed coyotes.
THE ISSUE IS WITH PETS
suspicious coyote mother and a dog owner not being vigilant
Whereas coyotes don't approach humans, dogs are a different story because of territorial issues and because of prey issues. In many ways, coyotes and dogs look alike, but coyotes and dogs are naturally antagonistic towards each other. Remember that coyotes keep other coyotes out of their territories. Coyotes are also both curious and suspicious of dogs: they may feel compelled to come in closer to investigate. Always supervise your pets to prevent incidents: the minute you see a coyote, leash and go in the other direction. Most dogs have a tendency to go chasing after coyotes. Please don't allow your dog to do this.
coyote messaging a dog — the dog should have been kept away from the coyote
Coyotes have approached dogs. If they get too close, they could either grab a small dog or "message" a larger dog who the coyote considers a threat to its territory or its personal space. They can only do this when they get close enough. Don't let them. You can prevent an incident by keeping your dog away from coyotes in the first place, by leashing when you see one, and by walking away from it. It's no different than when you encounter a skunk with its tail up: keep your dog off of it, and move away from it.
coyote following
IF, inadvertently or by surprise, a coyote gets too close, that is when to scare it off, otherwise just walk away without running: see http://baynature.org/article/how-to-get-along-with-coyotes-as-pups-venture-out/
Coyotes may follow dogs to find out what the dog is doing and where it is going (they do the same to non-family coyotes). If you and your dog are moving away from the coyote, and away from any denning site, the coyote soon will no longer follow. If you don't want the coyote to follow at all, toss a small stone in its direction (not at it), and/or approach it (but don't get too close) using your own blatantly angry body language and angry yelling. Noise alone, or waving flailing arms, is not always effective in making a coyote move — something has to move towards the coyote. And it isn't going to help if you are too far away. You've got to get within the coyote's critical distance — at most 50 feet — and you have to be assertive about it. Walking towards the coyote while slapping a newspaper viciously on your thigh works, but tossing stones towards it is probably more effective. However — and this is a very important "however" — if the coyote doesn't budge, it is probably protecting a nearby den site. In this case, turn around and leave. Do not provoke an incident. See the above link in Bay Nature.
It's always best to be proactive in keeping a coyote away. The minute you see a coyote, leash up and move away from it, and know how to shoo it off effectively if it comes closer to you than 50 feet.
Note that practically all scratches or bites by coyotes to humans are due to feeding the coyote, or to an owner getting him/herself between a coyote and a pet, so don't do these things. And, never run from a coyote: this activity actually initiates the chase response in a coyote who may also nip at your heels. They also sometimes nip at car tires when the car is in motion. The phenomena is called "motion reactivity".
ENCOUNTERS CAN BE SCARY
Encounter: the dog chased the coyote and the coyote stood up for itself
Encounters CAN be scary if you are unprepared and don't know what to expect or what to do. Please learn what coyotes are like, not what you think they "should" be like — for instance, that they don't "fear" humans but are "wary" of them, and not that "coyotes should be heard and not seen". By knowing their true normal behaviors, and by knowing what to do *IF* they approach your dog, you will be informed and you will not be so fearful. For starters, watch the video, Coyotes As Neighbors: https://youtu.be/euG7R11aXq0, which will spell out normal coyote behavior and what you can do to keep coyotes away from a pet.
MANAGING COYOTES
The number one method of managing coyotes for coexistence is through human education and human behavior modification: that is what this posting is trying to help with. These have been shown to be extremely effective. The City of San Francisco has been lax in putting out signs or getting educational material to folks. Some of us have been filling the void, getting material, information and guidelines out to people, but as individuals or as small organizations, we have not been able to reach everyone. Please visit coyotecoexistence.com for specific information, and coyoteyipps.com.
Many cities have coexistence policies — they all work when folks abide by the guidelines. BUT, as with car driving laws, even if you know them and follow them, there will be some fender-benders that might be frightening. We have fewer than 100 coyotes in the City; the number of dogs is in the 250,000s. There is bound to be an incident now and then.
The number of real coyote incidents in the City is not many. There have been less than a handful of dog fatalities by coyotes — all were unleashed small dogs in known coyote areas — all were preventable. There have been many incidents of people being frightened and reporting "attacks" on their dogs. Few if any of these attacks were reported on a questionnaire which would tease out what actually occurred. Instead, these incidents have been spelled out on the social media with warnings of doom that is awaiting us all.
Most of the sightings of coyotes have been reported as charming. But there have been some fearful encounters, and recently groups of dog owners in some of the parks have turned decidedly against them. Social media tends to perpetuate, spread and amplify the fears, and encounters are inevitably worded as deliberate "aggressive attacks". For instance, recently, there was a report of an attempted "attack" on a dog at 5:30 in the morning. However, a lone coyote, who weighs 35 pounds, is not going to "attack" a 130 pound Mastiff… Coyotes may watch dogs, follow, or hurry in your direction for many reasons, including curiosity, or investigation. They may jump up and down because of anxiety. These are not "attacks", nor are they "attempted attacks". Hopefully, by learning about coyotes, we can diminish the very real feeling of fear which comes from not knowing what is going on.
a coyote standing on a pathway, watching
Our Animal Care and Control Department has had many people report "aggressive" coyotes: but when questioned further, the majority of these reports were of a coyote just standing, or doing nothing but looking at the purported victim.
Two years ago I watched a man, straight faced, tell me that he had been frightened "out-of-his-wits" by a monster 100-pound coyote just a few moments before seeing me. He was visibly shaken. He hadn't seen me watching the whole incident a little way down the path. The incident involved his dog chasing a coyote. The coyote turned around to face the dog. When the dog ran back to its owner, the coyote proceeded on to where it had been going. But the owner was left frightened, and justified his fright by saying it was a "monster 100-pound coyote". If the dog had been leashed, the incident would not have happened. It happened in a park where everyone knows there are coyotes.
If you have questions, or if you want help with specific issues, please contact me or anyone at coyotecoexistence@gmail.com
"Didn't Mom Tell You Not To Play With Your Food?" & Dad Steals The Meal
by yipps:janetkessler in "toying" with prey, coyote behavior, coyotes, family interactions, father coyote behavior, feeding, parenting, social interactions
This was absolutely entertaining to watch today! Little female yearling wanders off to hunt from the area where her Dad had stationed himself to keep an eye on things. She works hard and is extremely patient, which pays off: she succeeds in catching some prey after about 15 minutes of intense effort, and immediately kills it.
Instead of eating the prey right away — an indication that she was not terribly hungry — she plays with her catch for a few minutes, tossing it up in the air, catching it, pouncing on it, and generally just having fun. "Didn't Mom tell you not to play with your food?" A friend of mine suggested this might be a good descriptive title for this posting.
When I was a kid, if you could get away with it, much more fun than eating was to see how high you could stack the peas, form a dam in the potatoes and break it so the gravy would run out, make the chicken wing work, organize the carrot sticks in geometrical patterns, spread everything around so it looked like you had eaten most of it. "Don't play with your food" we were told, but no reason was ever given.
Today I noted that there might be something to that rule! Within a few minutes, Dad came walking over from his lookout post. "There's Dad! I'll show him what I can do!" The youngster tossed the prey high up in the air one last time and tumbled over in the process, with Dad watching and closing in. The prey flew up in the air and landed on the other side of Dad.
Dad approaches
Dad eyes the prey
"Look, Dad, at what I can do!"
Daughter tumbles over
Hmmm, the prey is over there.
Dad goes for it and gets it.
We all know that coyotes are opportunistic, and here was an opportunity! Dad grabbed the food that had been tossed and ran off with it! And he ate it up! The thief!! Might there be a moral to the story?
Dad dashes away with what is now his.
Dad increases the distance
Daughter comes to watch
Daughter watches him eat
Dad scratches himself on a bush
All is forgiven. Daughter grooms Dad to show there's no ill will.
And the youngster watched, somewhat bewildered! Dad then scratched himself by pushing his back against the stiff branches of a bush, and then both coyotes headed over to where the prey had been found in the ground. But there was nothing else to be had from that location. Ahh, that's life!
The youngster turned to Dad and began grooming him. All appeared to have been forgiven, and maybe even forgotten! The female hadn't been hungry anyway, right?! Then, they both headed off into the bushes.
Following Mom, by Charles Wood
by yipps:janetkessler in coyote behavior, coyote living areas, coyotes, evading, family interactions, following, hiding, intelligence, mother/pup learning, reactions to a human
Pup1
Both photographs are of my LA county pup following Mom around. Both were alarmed when they saw my companions, another human and two good sized dogs, and me. Mom headed down the road and within a minute her puppy followed. The road offered us a clear view of them, but for only parts of the way because brush along the road at times concealed them from view. Soon both coyotes were hidden. Yet Mom could have immediately hid with her puppy in the brush. Why didn't she? I think she had decided it was to her advantage to use the road strategically.
When Mom took to the road, I didn't know if she intended to approach or avoid. I think she knew that by taking to the road, I wouldn't know where she would end up or whether she intended to come towards me or intended to go away. All I would really know was that she was on the move.
PupMom
After dusk, Mom came out from hiding to sit and stare at us, her puppy still in the brush. A third coyote, Dad, came in and out of view near them. Together, Mom and Dad formed a stone wall against an intrusion. Then, apparently instantly oblivious to danger, the puppy decided to come out and join Mom. Mom got up and the puppy followed her back into the brush. The puppy is too young to know that Mom doesn't want to play when actively guarding the family.
Posting written by Charles Wood. Visit Charles Wood's website for more coyote photos: Charles Wood. His work is copyrighted and may only be used with his explicit permission.
Rainy Dawn — in Sepia
by yipps:janetkessler in coyotes, photography
It was wet, wet, wet outside, so, of course, when I came across coyotes making their rounds, they, too, were wet, wet, wet. These semi-silhouette photos were taken under very bad early and gloomy light conditions. My ISO must have been about 6400. Nevertheless, the individual fur strands stood out sharply against the background sky and I thought their forms on the rocks were absolutely beautiful. Under those lighting conditions, there really was no "color" in the photos, so I played with some "enhancement" possibilities and decided that sepia showed these forms off to advantage.
Rock formations and outcroppings exist in a great many of our Bay Area parks: these are mostly chert, but there are also a few serpentine formations.
Rottweiler Harasses Coyotes
by yipps:janetkessler in blatant visual message, coyote behavior, coyote reactions to dogs, coyotes, coyotes and dogs, coyotes defending themselves, dog reactions to coyotes, harassment by other animals, human behavior, territoriality, video
I have seen the kind of activity in this video too often. Our Animal Care and Control Department, ACC, points out that some individuals continue to allow their dogs, "off-leash in active coyote areas despite education, posters, flyers, signs and barriers all warning dog owners to abide by the law and keep their dogs on-leash, or, better yet, avoid the marked areas entirely." So a few irresponsible individuals are setting themselves up for unexpected coyote encounters by not following the simple rules. The only method to keep coyotes and dogs apart is to leash the dog in a coyote area. If you and your dog see a coyote, walk in the opposite direction, not towards it.
We are lucky to have an Animal Care and Control Department which is taking a proactive stance to protect both our native coyotes and companion pets. ACC has recently cordoned off areas and instituted temporary park closures — they have been forced into doing this because a few dog owners continue to be irresponsible towards their pets and our wildlife, putting both at risk.
People have asked about "relocating" our coyotes — this is not an option since another coyote would just fill the vacant niche left behind, and relocation is a death sentence for any moved coyote. Coyotes are here to stay and the community needs to learn how to peacefully coexist with them. Ninety-nine percent of everyone I speak to loves having coyotes — a bit of the wild — in our urban parks. It brings back something that they've been out of touch with for too long. Note that it is only a few individuals who are irresponsible. Please be a responsible pet guardian: leash your dog in a coyote area or visit parks which do not display coyote warning signs. We only have ten coyotes in the city — it doesn't take a lot of effort to coexist with them.
Winter Comes To L.A., by Charles Wood
by yipps:janetkessler in coyotes
I've been watching my Los Angeles county coyote family since 2009. I watch them during outings with my camera and my dog, Holtz. In the spring and summer I see them frequently. In fall and winter I rarely do. I usually spend a couple hours waiting for them to appear, viewing them only for a few minutes. If they linger, it is to scold Holtz and me.
I saw one Sunday at dusk and took its picture. I had just arrived in their field. The coyote spotted me as it came down a dirt road 200 yards to the south. It ran full speed and stopped about 100 feet from Holtz and me. It yipped and scraped as I took its picture. A few minutes later it was still yipping as I walked on the road back to my car. Which one of my coyotes was it?
Sadly, it wasn't Dad. It has been more than three months since I last saw him. Six months before that, he was a healthy looking adult male. When I saw Dad in August he looked thin, scraggly, and old. It broke my heart to see him ailing and my instincts told me to let him go. I'll know Dad is dead if he isn't with Mom next pupping season. If I see him sooner, I'll be the only one seen rejoicing because Dad doesn't like me and he and Holtz have issues.
It wasn't Mom, lacking a cauliflower ear. It wasn't Mister, Dad's yearling son, the lower lip being wrong. If male, it could be brother Tom. If female it could be Bold, but not sister Shy because Shy is smaller. My guess is that the coyote knew Holtz and me. When it saw us it ran up to scold us. All of my coyotes scold us; coyotes that don't know us just leave. Still, it could be a new coyote, perhaps a new mate for Mom.
Earlier Sunday, I spoke with a man about my coyotes. He said he walks near their field regularly and sees them, though lately not so much. I asked him if he recognized them as individuals and he seemed to say yes. I asked him if he knew the mom, distinguishable by her cauliflower ear. He looked at me saying, "I don't know them that well". A nice man who stays on the trails, my coyotes know him as well as they need to. They have to know me a little better than that.
Posting written by Charles Wood. Visit Charles Wood's website for these and more coyote photos: Charles Wood. His work is copyrighted and may only be used with his explicit permission.
by yipps:janetkessler in coyote behavior, coyotes, disappearing, evading, hiding
For three full hours this coyote was able to avoid being seen by anyone at all except one man who said he thought he might have seen it, but wasn't sure! The coyote picked times to move around when there was little activity. When it heard or saw someone, it slipped casually into the bushes — there was no quick movement which might have drawn one's attention to it, so people simply did not notice. When there were not enough bushes around to "slip into", ducking casually behind one, so as to be partially hidden, worked. At one point, on parallel paths separated by greenery, the coyote simply stood absolutely still and watched, until the "danger" on the other parallel path had passed, and then continued on its slow trek. When it stopped to relax, it did so in tall grasses or against shrubbery or far enough away from the beaten path so as not to draw attention to itself. Most importantly, it moved slowly or stood absolutely still — walkers and runners would go by without noticing the coyote at all.
Of course, this is not always the case. Sometimes a coyote gets unlucky and is seen — and people like to tell others what they have seen so word spreads. But also I have seen coyotes who allow themselves to be very conspicuous at times — seemingly on purpose. They do so most often by picking a dog-walking time for an excursion or to check things out. And then there is always the surprise encounter when someone suddenly appears on the path ahead. If there is a dog involved, a coyote will stop its activity and look at the dog until it passes, and then continue with whatever it had been doing and wherever it had been going.
"Mighty Aggressive" is simply not what is going on.
by yipps:janetkessler in coyote behavior, coyotes Tags: coyotes, urban coyote behavior, urban coyotes
I advised some dog walkers that a coyote was around a bend. They ignored me until the coyote was at the top of the hill and could actually be seen. One of the women turned to me and said "mighty aggressive I would say". I asked why she thought this — the coyote was just standing on the same path as she was.
I had been watching the coyote hunt, and it just happened to be headed in the direction of the walkers. It couldn't possibly have seen the walkers to avoid them, just as the walkers could not possibly have seen the coyote. The woman turned to me and said that the coyote was obviously after them — if he hadn't seen them, he surely could have HEARD them, and, weren't coyotes SUPPOSED to be afraid of us? Didn't that constitute aggression?
No, that does not constitute aggression.
And no, coyotes are not necessarily fearful of people — rather, it would be more accurate to say that coyotes are WARY of people. They will do their utmost to avoid people. But closer encounters in a park will happen now and then. The coyote may look at you, and may even study you for a moment — that is not aggression — that is curiosity, or even surprise. And then he will move away. Coyotes are not at all interested in people. In this case, the coyote came within about 50 feet of the woman and her dog which was leashed. Both parties gazed at each other for a moment and then the coyote ran off the path.
Recap of dog/coyote behavior: Though not frequent, instances of dog/coyote encounters have occurred. A short leash and walking on can prevent an incident. Coyotes have shown an interest in some dogs — dogs and coyotes, after all, are very similar in appearance. Young coyotes have expressed degrees of curiosity about dogs, and even attempted friendly play — but they remain skittish and ready to flee at the slightest startle.
However, parents tend to be defensive of their territories and their young, and they prefer greater distances between themselves and dogs. If your dog comes too close, the coyote — especially if it is an alpha — may feel threatened and act accordingly, with definite and clear MESSAGES to your dog. These messages progress from a very cat-like defensive posture: arched back and snarly face, to a short charge-and-retreat sequence, and, ultimately, it may attempt to nip the dog at his haunches — trying to herd it away, in the same fashion that cattle dogs do. When they do so, they are not attempting to do anything more than TELL the dog something in the only way they can: " go away", "give me space". Keeping your dog on a short leash and moving on and away from the coyote helps guard against this type of coyote reaction in an unexpected encounter. You may have to go so far as to flail your arms and yell at the coyote to back off.
Your dog may want to chase or play with a coyote it sees, or may even feel a need to protect you against a wild animal it is not sure about. It is important to keep your dog next to you and calm, and to walk away quickly before there is time for a possible antagonistic communication to escalate if it has already begun. By doing this, you are messaging your own disinterest in the coyote. But do not run because running might be interpreted as an invitation for the coyote to chase you.
Coyotes have run after some dogs, seemingly unprovoked by the dog himself, and exhibited the messaging behaviors I mentioned above. As far as I have seen, this always occurs when there has been previous chasing by the dog or antagonistic communication between the two — a communication few humans are aware of. Dogs and coyotes communicate exceeding effectively through eye contact and body language. In addition, highly spirited dogs — as many small dogs are — seem to raise the ire of some coyotes: Coyotes seem to want the dogs passing through their territories to be fairly calm: a super active dog is cause for alarm, and this assessment extends to as well to transient or interloper coyotes. The oddest behavior of a coyote towards a dog that I've seen was a coyote who slowly followed a dog which was trailing behind its owner — stretching to reach the dog's tail as if it were "daring" itself to do so. The owner turned around just as the coyote reached the dog and simply said "go away", pointing his finger instructively at the coyote, and the coyote did so!
So, please keep your dog next to you and walk on when you see a coyote! And if you need to tell a coyote who has come much too close not to come closer, you can do so by flailing your arms to make yourself appear larger, making sharp loud noises, or tossing pebbles in the coyote's direction — not at him — to warn him off. Both people and coyotes want the same thing: space! We need to understand their methods, and we need to know what methods will work for ourselves.
Nose Punch
26 Sep 2011 1 Comment
by yipps:janetkessler in coyote behavior, coyotes, hunting, video Tags: coyote, coyote behavior, coyotes, urban coyotes
A hard and fast "punch" is delivered at the entryway to the burrow of a little critter that will become the coyote's prey. It's part of the cycle of life. Coyotes sometimes use their two front paws which they stiffen for this purpose. In this case, the nose is used to deliver the hefty punch. From what I have seen, this punch disables or weakens the critter. Most of the time, as here, it is followed by probing and digging before the prey is actually captured. The coyote regularly looks around to check out the safety of his surroundings.
Wrong Tree?
by yipps:janetkessler in coyote behavior, coyotes, video Tags: coyotes, urban coyote behavior, urban coyotes
I, too, heard the loud rustling sounds of a squirrel which caused me to look over and see it. The coyote's attention became more and more intent the more he watched the loud activity. Finally, the coyote stood up, then dashed over to the tree. But no squirrel was in sight. "Could I have mistaken the tree?" Just in case he got it wrong, the coyote inspected the next tree over, but the squirrel was not there either, apparently. So Coyote settled for a green grassy salad close by before trotting off.
Chicken Drama, But No Drumsticks!
by yipps:janetkessler in coyote behavior, coyotes, video Tags: coyote behavior, coyotes, urban coyote behavior, urban coyotes
coyote hears early morning chickens
chicken alarmed at seeing coyote
chicken flies the coop, landing in a nearby tree
the dog barked
coyote watches chicken in a tree
waiting gets tiring
chicken flies back to fenced yard
coyote departs
This was an exciting day! Many people keep chickens in their yards these days: chickens are allowed, but not roosters because they crow. But guess what — it is not just the roosters who crow! So crowing is what I heard, and so did this coyote as he passed through a neighborhood. The coyote approached the very well fenced-in yard — there was no chance of him getting in. However, the chickens saw the coyote through the wire fencing and began shreaking and flapping. One flew to the top of the fence where she strutted for a few minutes, and then she flew out of the protected yard into a tree in the overgrown yard next door. I thought: Oh, no!
The dog did his duty by barking at the intruder, but he was fenced in and that is all he could do, so he left. The coyote walked over to under the tree where the chicken had flown. And he waited. And he waited, hoping the chicken would descend to a more reachable level. The chicken crowed continually the entire time, but never budged from her high perch in the tree. And the coyote waited and waited. I wondered if the chicken would make it back. She did. She suddenly flapped her way back after about 35 minutes. As she did so, the coyote jerked to a standing position, but remained where he was, watching.
Maybe chickens are smarter than we think. My thought is that this chicken had flown out of the coop to distract the coyote from the other chickens. She stayed out there scolding that coyote. When she realized the coyote could not reach any of them — which the coyote would have done by then — she flew back to the safety of her yard. Eventually, the coyote walked off. He knew the chickens were not reachable in their yard. There was lots of drama, but no drumsticks this time!
Mmmm: Chile Con Queso!
Urban life has a lot to offer, including a greater variety of menu offerings that can be found right down the street or around the corner. This meal must have been delicious — the coyote licked the bowl and spoon clean after first eating a tortilla chip. Then he looked up and down the street for more signs of food. There not being any, he trotted off into the woods. Although these were tossed-out-the-window leftovers, there was enough there for the coyote to appreciate the taste, and maybe to decide he would like more.
This kind of treat is only ever found in areas of human activity. I've seen coyotes wander into picnic areas after hours where they pick up bits of food which cannot be found in wild habitats. Aren't we trying to keep coyotes from frequenting human activity areas? By dumping our dirty paper plates and leftovers wherever we please, we are actually inviting these critters to come out into the open more.
Watching The Ducks Overhead
A flock of ducks passed overhead and I watched it across the entire skyline. A coyote I had seen not too far off also had stopped its activity to observe the same sight, raising its head and fixing its gaze on the arcing flight of birds.
We both stayed there watching until the birds were no longer in sight, and then continued what we had been doing before we saw them: me, watching the coyote, and the coyote hunting.
Coyotes are as curious and as interested in their surroundings as we are. I frequently see them watching simply to see what is going on. I felt "connected" to have shared the same awareness as a little wild coyote had.
Sniffing For, then Scratching At an Irritant
by yipps:janetkessler in communication, coyote behavior, coyote reactions to dogs, coyotes, dog reactions to coyotes, oneupmanship Tags: coyotes, urban coyote behavior, urban coyotes
This fellow had been relaxing when he suddenly bolted up and looked into a neighbor's yard, then trotted over and stood behind some thick growth and sniffed intently, with his nose high in the air. He spent a full minute doing this, closing his eyes sometimes as if to really savor what might be in the air. He was in an overgrown empty field, and directed his sniffing towards the yard next door where several dogs lived. These dogs were never out of their house without their owners. However, I had seen one come over to the overgrown field to do its business and I had seen this particular coyote sniff out these messes and urinate on top of them. Also, I've seen one of the dogs chase this coyote, though not in a very intense manner. These dogs are particularly acute at either hearing or smelling coyotes that come to the property: at the slightest hint that a coyote might be around, one and then all of them will begin barking together. I think there are four dogs who live there, on and off.
On this day, no dogs were around. The coyote sniffed carefully from a long distance away, and then slowly trotted closer to the hedge which divides the properties — yawning on the way over. I think coyotes sometimes yawn to maintain a casual-calm mood for themselves. At the hedge-line, the coyote stopped and stretched its neck up to get a better view. Again, no dogs in sight, and no barking. So the coyote carefully and slowly entered the yard, walked around casually, found the smell he was looking for, urinated on the spot, and then kicked and scratched that area of ground where he had urinated. The coyote had probably found a spot where one of the dogs had urinated. "Take that!" It was one of those "oneupmanship" behaviors directed towards the dogs which have been an irritant to the coyote. When done, the coyote exited the yard and continued trekking through uninhabited areas before disappearing.
A Feast For One At A Time
by yipps:janetkessler in coyote behavior, coyotes, group activity, hunting Tags: coyotes, urban coyote behavior, urban coyotes
looking away while the other feasts
Peeking at the eater
onlooker diverts face to avoid gaze when faced directly by the one feasting
onlooker keeps eyes off of eater
eater gives a warning to onlooker
onlooker gets severe warning
onlooker growls back defensively
onlooker moves away
feasting coyote gets to finish undisturbed
This posting shows two coyotes feasting on a larger prey than normal. It is a skunk which, when I came upon the scene, was already dead. The above sequence of photos shows only the first coyote eating. The other one hung around, avoided looking at the one feasting, succumbed to looking, tried moving closer. The feasting coyote then warned off this onlooker. She was going to have her fill before allowing the other one to come in and she became nasty about it to make him understand, showing her teeth and pulling back her lips. This part of the sequence I've posted in the above gallery.
The gallery below shows the second coyote who decided to move about 50 feet away from the feasting coyote. At this distance of removal, he briefly, and jealously, glanced back at the one feasting before settling down. He then kept his gaze away from the feasting coyote, appearing disinterested, but in truth, patiently waiting his turn to eat. When the first coyote had finished and walked off, this second guy immediately hurried to feast on the second pickings. He ate a bit and then dragged the carcass off before eating some more.
departed coyote moves off 50 feet and looks back
departed coyote waits patiently looking the other way
feasting coyote departs
departed coyote returns quickly
the second coyote now eats
second coyote drags the carcass off
This website reflects my 13+ years of intense, careful, and dedicated field-work — empirical observations — all photo-documented without interfering or changing coyotes' behaviors. Be welcome here, enjoy, and learn!
Note that none of the coyotes I document and photograph is "anonymous" to me: I know (or knew) each one of them, and can tell you about their personalities, histories, and their family situations. There have been almost 100 of them, distributed among over a dozen families, all in San Francisco. Images and true stories have the power to raise awareness and change perspective.
© All information and photos in my postings come from my own original and first-hand documentation work which I am happy to share, with permission and with properly displayed credit: ©janetkessler/coyoteyipps.com.
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Urban Coyote Myth: Coyotes Luring Dogs to Their Deaths
What Would Be The Outcome In a Coyote/German Shepherd Altercation? by Charles Wood
Coyotes yipping: Coyote behavior
Safety Around Coyotes; PLUS Behaviors to be aware of if you have a dog: Updated
Coyote Den In A Backyard
Coyotes Use Dens Only For Pupping
Mom Tells Off Her Son, and Dad Stands By
How Far Can You Hear A Coyote Howl?
Coyotes: What to Know and Do
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Coyotes: Beyond The Howl
EXHIBIT: Coyotes, Beyond the Howl
Family First: Wily Coyote's Here to Stay, by Linnea Due
How To Coexist With Wild Coyotes — From SF's Own 'Coyote Whisperer'
How to get Along With Coyotes As Pups Venture Out, Bay Nature
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Janet Kessler: The Urban Coyote Watcher, by Leath Tonino
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redpajama_set_name: RedPajamaCommonCrawl


… Now that we know what the problem is, here is my solution. Like we did with the link texts years ago on the web, we should visually distinguish 3D Touchable buttons. Look at this same screen and see if you can tell which toggles accept 3D Touch … My solution is adding a line on bottom-right of things that can be 3D Touched. Let's call them Force Decorators (with reference to Force Touch). 3D Touch is missing the most obvious thing to be mainstream. Visual cues. I think this is the answer.
Simple, elegant, and almost certainly correct; if you do support 3D Touch, consider adopting that!
….recently I needed to have an UIGestureRecognizer to apply to any UIView that intercepts 3D Touch as you can do with tap, drag, etc, but nothing similar is available in system libraries.
In my last post I wrote about introducing 3D Touch as common UIGestureRecognizer in any UIView to improve the interaction with your app, now I want to explore the haptic feedback which is giving us a new physical way to give control to the user of what is happening on his iPhone.
Until haptic feedback through taptic engine, play sounds were the only way to provide users a feedback about an action in the app, but sounds are annoying and sometimes creepy.
So, before designing your power user gesture interfaces going forward, check out those technology comparisons … and especially the 3D touch design/usability postmortems. Nothing worse than wasting time writing features that nobody actually uses!
Remember back when we first collected articles on 3D touch, and digital scale apps were a nifty thing? Guess that's going to go by the wayside as 3D Touch falls off as well. If you do have one of those apps, maybe you want to migrate to Android — check out the state of their art in 5 Best Real Digital Scale Apps for Android!
The source and example project is up on github; grab and enjoy!


text:
BCS Financial Group () is a Russian financial service company. It was established in 1995.

The group was established by Oleg Mikhasenko in Novosibirsk and was originally known as BrokerCreditService. Initially focusing on retail banking activities, by the mid-2000s it started competing with Moscow-based brokers. By 2013 it was the largest trader of equities and derivatives on the Moscow Exchange. BCS launched Russia's first dark pool trading system.

In 2013 the group moved its emerging market operations from Cyprus to London.
In 2016 it was assigned a B− long-term credit rating by Standard & Poor's.

References

External links

Financial services companies of Russia
Financial services companies established in 1995
Banks established in 1995
Companies based in Novosibirsk
Russian investment banks

redpajama_set_name: RedPajamaWikipedia


text:
Multirate PWM balance method for the efficient field-circuit coupled simulation of power converters
Andreas Pels ORCID: orcid.org/0000-0003-1517-484X1,2,3,
Herbert De Gersem ORCID: orcid.org/0000-0003-2709-25181,2,
Ruth V. Sabariego ORCID: orcid.org/0000-0001-7515-39233 &
Sebastian Schöps ORCID: orcid.org/0000-0001-9150-02191,2
Journal of Mathematics in Industry volume 9, Article number: 8 (2019) Cite this article
The field-circuit coupled simulation of switch-mode power converters with conventional time discretization is computationally expensive since very small time steps are needed to appropriately account for steep transients occurring inside the converter, not only for the degrees of freedom (DOFs) in the circuit, but also for the large number of DOFs in the field model part. An efficient simulation technique for converters with idealized switches is obtained using multirate partial differential equations, which allow for a natural separation into components of different time scales. This paper introduces a set of new PWM eigenfunctions which decouple the systems of equations and thus yield an efficient simulation of the field-circuit coupled problem. The resulting method is called the multirate PWM balance method.
Switch-mode power converters are used in various devices from small-scale applications like mobile phone chargers to industrial large-scale applications like welding devices [7]. These converters use transistors to switch on and off the input voltage to produce an output voltage, which, in average, has the desired amplitude. A filter circuit is used to smoothen the output. The simulation of these devices is computationally expensive since, through the transistor switching, steep transients occur in the converter. Furthermore often a switch-event detection is necessary to avoid step size rejection or even solver failures [14]. A multirate method has been developed in [9, 10] which uses the concept of Multirate Partial Differential Equations (MPDEs) [3, 12] and a combination of a Galerkin ansatz and conventional time discretization to efficiently solve problems with pulsed excitation. The method is applicable to power converters in which the switching behavior is idealized and known a-priori. It is particularly efficient in the case of linear elements. Some circuit elements may only be accurately represented by field models. For example the induced currents in the conducting materials of an inductor usually cause eddy current losses, which can easily be accounted for in a field model but not in a circuit model. In this paper the multirate method from [9, 10] is applied to a linear buck converter circuit (see Fig. 1) in which the inductor is represented by a 2D finite element model. This substantially increases the size of the strongly coupled system of equations. To still ensure an efficient simulation, a basis transformation is applied to the pulse-width modulation (PWM) basis functions [5] leading to decoupled systems of equations which can be solved efficiently in parallel. The resulting method is called the multirate PWM balance method in analogy with the harmonic balance method where harmonic functions take the place of the PWM basis functions. Numerical results on the buck converter show the efficiency and accuracy of the proposed method in field-circuit coupled problems.
Simplified circuit of the buck converter in continuous conduction mode with \(C=10~\text{$\mu $F}\) and \(R=30~\varOmega \). The field model of the pot inductor (axisymmetric around z-axis) is designed to have an inductance of \(L=65~\text{mH}\) and a series resistance of \(R_{\mathrm {L}}=800~\text{m$\varOmega $}\) at DC. The figure shows the equipotential lines of the magnetic vector potential
The paper is structured as follows. Section 2 introduces the concept of MPDEs and explains the solving procedure using Galerkin approach and conventional time discretization. Subsequently Sect. 3 presents the original PWM basis functions as described in [5]. In Sect. 4 the PWM eigenfunctions are developed and their advantageous properties for the solving process are highlighted. Finally Sect. 5 summarizes numerical results and compares the three different solution approaches, i.e., conventional time discretization and the MPDE approach with PWM basis functions on the one hand and PWM eigenfunctions on the other hand. The paper is concluded by summarizing its content in Sect. 6.
Multirate formulation
Let the field-circuit coupled model [13] of the converter be described by the system of ordinary differential or differential-algebraic equations
$$\begin{aligned} \mathbf {A}\, \frac {{\mathrm {d}}}{{\mathrm {d}}t}\mathbf {x}(t)+\mathbf {B}\, \mathbf {x}(t) = \mathbf {c}(t), \end{aligned}$$
where \(\mathbf {A}\in \mathbb{R}^{N_{\mathrm {s}}\times N_{\mathrm {s}}}\) is a possibly singular matrix, \(\mathbf {B}\in \mathbb{R}^{N_{\mathrm {s}}\times N_{\mathrm {s}}}\) is assumed to be a regular matrix, \(\mathbf {x}(t)\in \mathbb{R}^{N_{\mathrm {s}}}\) is the unknown solution, \(\mathbf {c}(t)\in \mathbb{R}^{N_{\mathrm {s}}}\) is the excitation, and \(t\in (0, \mathcal {T}]\) is the simulation interval. The initial state of the model is given by consistent [6] initial values \(\mathbf {x}(0)=\mathbf {x}_{0}\). The ideal pulsed excitation
$$ v_{\mathrm {i}}(t)=\textstyle\begin{cases} V_{0} & \text{for all } \tau (t) \leq D, \\ 0 & \text{otherwise}, \end{cases} $$
is used as input of the power converter circuit. We denote by \(\tau (t) = \frac{t}{T_{\mathrm {s}}} \text{ modulo } 1\) the relative time, \(T_{\mathrm {s}}\) is the switching cycle and D is the duty cycle.
The system of Multirate Partial Differential(-Algebraic) Equations (MPDEs or MPDAEs) with two time scales corresponding to (1) is given by [3, 11, 12]
$$ \mathbf {A}\biggl(\frac{\partial \mathbf {\widehat {x}}}{\partial t_{1}} + \frac{ \partial \mathbf {\widehat {x}}}{\partial t_{2}} \biggr) + \mathbf {B}\, \mathbf {\widehat {x}}(t_{1},t _{2}) = \mathbf {\widehat {c}}(t_{1},t_{2}) , $$
where \(\mathbf {\widehat {x}}(t_{1}, t_{2})\) is the unknown multivariate solution and \(\mathbf {\widehat {c}}(t_{1},t_{2})\) is the multivariate excitation. Choosing the multivariate excitation such that \(\mathbf {\widehat {c}}(t,t)=\mathbf {c}(t)\), the solution of (1) and (3) are related by \(\mathbf {\widehat {x}}(t,t)=\mathbf {x}(t)\). Thus, the solution of (1) can be calculated solving the MPDEs and extracting the solution along a diagonal through the computation domain. To solve the MPDEs, additional conditions need to be specified. For the present application, a combination of initial and boundary values is applied. Initial values are supplied by \(\mathbf {\widehat {x}}(0,t_{2})=\mathbf {h}(t _{2})\), i.e., at \(t_{1}=0\), where h with \(\mathbf {h}(0)=\mathbf {x}_{0}\) is a function defining the initial values for all \(t_{2}\). The solution along the fast time scale \(t_{2}\) is periodic, i.e., \(\mathbf {\widehat {x}}(t_{1}, t_{2}+T_{\mathrm {s}}) = \mathbf {\widehat {x}}(t_{1}, t_{2})\). The multivariate right-hand side is chosen as \(\mathbf {\widehat {c}}(t_{1}, t_{2})=\mathbf {c}(t_{2})\), i.e., the pulses of the excitation occur along the fast time scale. It is possible to use MPDEs with more than two time scales. However, in the applications of this paper, it is not necessary and furthermore often not feasible since the dimension of the computation domain increases and thus also the computational effort to calculate the solution.
To solve the MPDEs (3), a Galerkin approach and time discretization is applied [2, 10]. The j-th solution component \({\widehat {x}}_{j}(t_{1}, t_{2})\) is approximated by expanding it into periodic basis functions \(p_{k}\) depending on the fast time scale \(t_{2}\) and coefficients \(w_{j,k}\) depending on the slow time scale \(t_{1}\)
$$ {\widehat {x}}_{j}^{\,h}(t_{1}, t_{2}) := \sum_{k=0}^{N_{\mathrm {p}}} w_{j,k}(t_{1})\, p _{k}\bigl(\tau (t_{2})\bigr) , $$
where the periodicity of the basis functions is accounted for by using the relative time \(\tau (t_{2}) = \frac{t_{2}}{T_{{\mathrm {s}}}} \text{ modulo } 1\). Applying the Galerkin approach with respect to \(t_{2}\) and over one period of the excitation \([0,T_{\mathrm {s}}]\) leads to
$$ \boldsymbol {\mathcal {A}}\frac{{\mathrm {d}}\mathbf {w}}{{\mathrm {d}}t_{1}} + \boldsymbol {\mathcal {B}}\,\mathbf {w}(t_{1}) = \boldsymbol {\mathcal {C}}(t _{1}) , $$
with block matrices \(\boldsymbol {\mathcal {A}}=\boldsymbol {\mathcal {J}}\otimes \mathbf {A}, \, \boldsymbol {\mathcal {B}}=\boldsymbol {\mathcal {J}}\otimes \mathbf {B}+\boldsymbol {\mathcal {Q}}\otimes \mathbf {A}\), where
$$\begin{aligned} \boldsymbol {\mathcal {J}}= T_{\mathrm {s}}\int _{0}^{1} \bar{\mathbf{p}}(\tau ) \, \mathbf {p}^{ \top }\! (\tau ) \,{\mathrm {d}}\tau ,\qquad \boldsymbol {\mathcal {Q}}= - \int _{0}^{1} \frac{{\mathrm {d}}\bar{\mathbf{p}}(\tau )}{{\mathrm {d}}\tau } \, \mathbf {p}^{\top }\! (\tau ) \,{\mathrm {d}}\tau , \end{aligned}$$
and right-hand side
$$ \boldsymbol {\mathcal {C}}(t_{1})= \int _{0}^{T_{{\mathrm {s}}}} \bar{\mathbf{p}}\bigl(\tau (t_{2})\bigr) \otimes \mathbf {\widehat {c}}(t_{1},t_{2}) \,{\mathrm {d}}t_{2} . $$
\(\bar{\mathbf{p}}\) denotes the complex conjugate of p and ⊗ denotes the Kronecker product.
PWM basis functions
The PWM basis functions developed in [5] are built up starting from the zero-th constant basis function \(p_{0}(\tau )=1\) and the piecewise linear basis function
$$ p_{1}(\tau ) = \textstyle\begin{cases} \sqrt{3} \, \frac{2\tau -D}{D} & \text{if } 0 \leq \tau < D, \\ \sqrt{3} \, \frac{1+D-2\tau }{1-D} & \text{if } D \leq \tau \leq 1, \end{cases} $$
which includes the duty cycle D of the excitation by construction. The higher-order basis functions \(p_{k}(\tau )\), \(2\leq k \leq N_{\mathrm {p}}\) are recursively obtained by integrating the basis functions of lower order \(p_{k-1}(\tau )\) and orthonormalizing them using the Gram–Schmidt algorithm. The generated basis functions are depicted in Fig. 2.
Original PWM basis functions \(p_{k}(\tau )\), \(k\in \{0,1,2,3,4 \}\)
For the PWM basis functions, the matrices \(\boldsymbol {\mathcal {J}}\) and \(\boldsymbol {\mathcal {Q}}\) from (6) are given by \(T_{\mathrm {s}}\) multiplied by the identity matrix (due to the orthonormality of the basis functions) and a square matrix with around 25% of non-zero entries, respectively. Solving the problem requires time stepping of the entire system (5).
PWM eigenfunctions
To enable an easy parallelization of the method, the equations (5) can be decoupled, for example by diagonalizing \(\boldsymbol {\mathcal {Q}}\), i.e., a basis transformation. We define new basis functions \(g_{k}(\tau )\) as linear combinations of the PWM basis functions, i.e.,
$$ g_{k}(\tau ):=\sum_{l=0}^{N_{\mathrm {p}}} v_{k,l} \,\, p_{l}(\tau ), $$
where \(v_{k,l}\) are unknown coefficients with \(k\in \{0, \dots , N_{\mathrm {p}}\}\), and \(g_{k}(\tau )\) are eigenfunctions of the time derivative operator
$$ \frac{{\mathrm {d}}}{{\mathrm {d}}\tau } g_{k}(\tau ) = \lambda _{k} \,\,g_{k}(\tau ). $$
We enforce this property in a weak sense by a Galerkin approach, i.e.,
$$ - \int _{0}^{1} g_{k}(\tau ) \frac{{\mathrm {d}}p_{m}(\tau )}{{\mathrm {d}}\tau } \,{\mathrm {d}}\tau = \lambda _{k} \int _{0}^{1} g_{k}(\tau ) \, p_{m}(\tau ) \,{\mathrm {d}}\tau , $$
where integration by parts and the periodicity of the basis functions is used. Inserting the expansion of the basis functions into (11) gives
$$ T_{\mathrm {s}}\boldsymbol {\mathcal {Q}}\,\mathbf {v}_{k} = \lambda _{k} \boldsymbol {\mathcal {J}}\,\mathbf {v}_{k}. $$
Since \(\boldsymbol {\mathcal {J}}\) is \(T_{\mathrm {s}}\) multiplied by the identity matrix (thanks to the orthonormality of the PWM basis functions), the \(\lambda _{k}\) and \(\mathbf {v}_{k}\) are the eigenvalues and eigenvectors of the matrix \(\boldsymbol {\mathcal {Q}}\), respectively. Furthermore since \(\boldsymbol {\mathcal {Q}}\) is real-valued and skew symmetric, and therefore a normal matrix, the eigenvectors \(\mathbf {v}_{k}\) are orthonormal. The new basis functions (complex-valued) are depicted in Fig. 3 for \(N_{\mathrm {p}}=4\). Note that the basis consists of pairs of conjugate complex basis functions.
PWM eigenfunctions \(g_{k}(\tau )\), \(k\in \{0,1,2,3,4\}\), i.e., \(N_{\mathrm {p}}=4\). (top) real part. (bottom) imaginary part
Inserting the transformed basis functions instead of the PWM basis functions into (6) and (7) leads, using the orthonormality of the eigenvectors, to
$$ \boldsymbol {\mathcal {A}}\frac{{\mathrm {d}}\mathbf {w}}{{\mathrm {d}}t_{1}} + {\widetilde {\boldsymbol {\mathcal {B}}}}\, \mathbf {w}(t_{1}) = {\widetilde {\boldsymbol {\mathcal {C}}}}(t _{1}) , $$
where \(\boldsymbol {\mathcal {A}}\) as in (5),
$$\begin{aligned} &{\widetilde {\boldsymbol {\mathcal {B}}}}=\boldsymbol {\mathcal {J}}\otimes \mathbf {B}+\boldsymbol{\varLambda }\otimes \mathbf {A}, \end{aligned}$$
$$\begin{aligned} &{\widetilde {\boldsymbol {\mathcal {C}}}}(t_{1})= \int _{0}^{T_{{\mathrm {s}}}} \bar{\mathbf{g}}\bigl(\tau (t _{2})\bigr) \otimes \mathbf {\widehat {c}}(t_{1},t_{2}) \,{\mathrm {d}}t_{2} , \end{aligned}$$
and Λ is a diagonal matrix with diagonal entries \({\lambda _{0}, \lambda _{1}, \dots , \lambda _{N_{\mathrm {p}}}}\). Thus the resulting matrices in (13) are block-diagonal and the degrees of freedom can be block-wisely decoupled. This leads to \(N_{\mathrm {p}}+1\) independent systems of equations given by
$$ T_{\mathrm {s}}\,\mathbf {A}\frac{{\mathrm {d}}\mathbf {w}_{k}}{{\mathrm {d}}t_{1}} + (T_{\mathrm {s}}\,\mathbf {B}+ \lambda _{k}\, \mathbf {A})\, \mathbf {w}_{k} = \int _{0}^{T_{{\mathrm {s}}}} \bar{g}_{k}\bigl(\tau (t_{2})\bigr) \,\mathbf {\widehat {c}}(t_{1},t_{2}) \,{\mathrm {d}}t_{2} \quad\text{for } k = 0,\dots ,N_{\mathrm {p}}, $$
where \(\mathbf {w}=[\mathbf {w}_{0}^{\top }, \mathbf {w}_{1}^{\top }, \dots , \mathbf {w}_{N_{\mathrm {p}}} ^{\top }]^{\top }\). Note that if a diagonal entry in Λ is complex, there is also a complex conjugate counterpart. The solutions of the decoupled system of equations corresponding to this complex eigenvalue and its conjugate complex counterpart, are, as a result, complex conjugate to each other. Therefore it is sufficient to solve one of them. This is similar to harmonic balance methods in which the harmonic basis functions are given by pairs of complex conjugates leading to similar systems of equations. In analogy to "harmonic balance method", we call the developed method the "multirate PWM balance method".
Test case and numerical results
The method is applied to the buck converter from Fig. 1, where the pot inductor is represented by a 2D field model with conducting core material (ferrite, \(\sigma _{\mathrm{fe}}=250 \) S/m). The coils are modeled as stranded conductors. The simulation interval is given by \(\varPsi =[0,10] \) ms. The switching frequency is \(f_{\mathrm{s}}=\frac{1}{T_{\mathrm {s}}}=1000 \) Hz. For the pulsed excitation (2) we use \(V_{0}=24 \) V. All calculations are performed in MATLAB. The partial differential equations governing the magnetoquasistatic problem are given by
$$ \sigma (\mathbf {r}) \frac{\partial \mathbf {A}_{\mathrm{m}}(\mathbf {r}, t)}{\partial t} + \nabla \times \bigl(\bigl(\mu (\mathbf {r})^{-1}\bigr) \, \nabla \times \mathbf {A}_{ \mathrm{m}}(\mathbf {r}, t) \bigr) = \mathbf {J}_{\mathrm {s}}(\mathbf {r}, t), $$
where r is the position vector, t is the time, \(\mathbf {A}_{ \mathrm{m}}\) is the modified magnetic vector potential [4], \(\mathbf {J}_{\mathrm {s}}\) are the imposed currents, \(\mu =4 \pi \times 10^{-7} \) H/m is the magnetic permeability and σ is the conductivity which is only non-zero in the ferrite core (\(\sigma _{\mathrm{fe}}\)). The problem is considered on a 2D planar domain with homogeneous Dirichlet boundary conditions.
Correspondingly, the Finite Element magnetoquasistatic [13] discretization of the magnetoquasistatic inductor model is given by the differential-algebraic system of equations [8]
$$ \mathbf {M}_{\sigma } \frac {{\mathrm {d}}}{{\mathrm {d}}t}\mathbf {a}(t) +\mathbf {K}\,\mathbf {a}(t) = \mathbf {P}\,i_{\mathrm{L}}(t), $$
where \(\mathbf {M}_{\sigma }\) is the singular conductivity matrix, K is the stiffness matrix, \(\mathbf {a}(t)\) gathers the degrees of freedom (DOFs) related to the magnetic vector potential, P is the discretization of the winding function [13] and \(i_{\mathrm{L}}(t)\) is the current through the inductor. The field-circuit coupling is expressed as follows. An additional variable is introduced for the magnetic flux linkage \(\varPhi (t)=\mathbf {P}^{\top }\mathbf {a}(t)\). All equations are coupled monolithically into the index-1 differential-algebraic system of equations [1]
$$\begin{aligned} &\mathbf {M}_{\sigma } \frac {{\mathrm {d}}}{{\mathrm {d}}t}\mathbf {a}- \mathbf {P}\,i_{\mathrm{L}}+ \mathbf {K}\,\mathbf {a}= \mathbf{0}, \end{aligned}$$
$$\begin{aligned} &\mathbf {P}^{\top }\mathbf {a}- \varPhi= 0, \end{aligned}$$
$$\begin{aligned} &\frac {{\mathrm {d}}}{{\mathrm {d}}t}\varPhi + R_{\mathrm {L}}\,i_{\mathrm{L}}+ v_{\mathrm {C}}= v_{\mathrm {i}}(t), \end{aligned}$$
$$\begin{aligned} &C \,\frac {{\mathrm {d}}}{{\mathrm {d}}t}v_{\mathrm {C}}- i_{\mathrm{L}}+ \frac{1}{R} \,v_{\mathrm {C}}= 0, \end{aligned}$$
which for the example in Fig. 1 contains a total of \(11\text{,}053\) DOFs. The initial conditions are given by \(v_{\mathrm {C}}(0)=0\), \(i_{\mathrm{L}}(0)=0\) and \(\mathbf {a}(0)=\mathbf{0}\).
The initial condition for the MPDEs (3) can be written as
$$ h_{j}(t_{2}) \approx \sum _{k=0}^{N_{\mathrm {p}}} w_{j,k}(0) \, p_{k}\bigl(\tau (t _{2})\bigr), $$
where \(h_{j}\) is the j-th element of h. It only has to satisfy the condition \(\mathbf {h}(0) = \mathbf {\widehat {x}}(0,0)=\mathbf {x}_{0}\). Consequently there is a high degree of freedom in choosing the initial values \(\mathbf {w}(0)\) for the system of equations (5). However not all choices lead to an efficient simulation, i.e., low dynamics in the slow time scale. The following choice of initial values has proven advantageous. First, the steady-state solution is calculated, i.e.,
$$ \mathbf {w}^{\,s}= \boldsymbol {\mathcal {B}}^{-1}\boldsymbol {\mathcal {C}}(0). $$
Secondly, the initial coefficients for \(k=1,\dots , N_{\mathrm {p}}\) are extracted from the steady-state solution \(w_{j,k}(0)=w^{\,s}_{j,k}\) for all j. The remaining coefficients are calculated by solving the solution expansion (4) for \(w_{j,0}(0)\) and using the condition \(\mathbf {\widehat {x}}(0,0)=\mathbf {x}_{0}\). In summary the initial coefficients are given by
$$ w_{j,k}(0)= \textstyle\begin{cases} w^{\,s}_{j,k} & \text{for }k=1,\dots ,N_{\mathrm {p}}\text{ and for all } j=1, \dots ,N_{\mathrm {s}}, \\ x_{j}(0) - \sum_{l=1}^{N_{\mathrm {p}}} w^{\,s}_{j,l} \,\, p_{l}(0) & \text{for }k=0 \text{ and for all } j=1,\dots ,N_{\mathrm {s}}. \end{cases} $$
The initial conditions for the system of equations (13) are computed similarly using the PWM eigenfunctions. Other choices of initial values may still lead to the correct solution but might impair the efficiency of the method.
To calculate the reference solution with a conventional adaptive time discretization, the MATLAB solver ode15s is used. It is modified to restart the simulation at the known switching instances. Consistent initial values for the restart of the solver are calculated by using a Newton–Raphson algorithm to solve the set of algebraic equations. The required differential variables are taken from the solution at the end of the prior solution interval. After finding the new set of initial values, the initial slopes of the differential variables are calculated by solving the subsystem of ordinary differential equations for the slope.
The multivariate solution \(\mathbf {\widehat {x}}(t_{1},t_{2})\) calculated using the multirate PWM balance method, i.e., solving (13) with ode15s, is reconstruced using (4) and the multivariate voltage at the capacitor is depicted in Fig. 4. The corresponding solution component of the original system of equations (1) is extracted along a diagonal through the computation domain. Figure 5 shows the current through the inductor along with the reference solution. The agreement between the multirate PWM balance method solution and the reference solution is excellent. The Joule losses in the core material due to eddy currents are calculated by
$$ P_{\mathrm{eddy}}(t)= \int _{\varOmega } \mathbf{E}(\mathbf {r}, t) \cdot \sigma (\mathbf {r}) \mathbf{E}(\mathbf {r}, t) \,{\mathrm {d}}\mathbf {r}= \bigl(\mathbf {e}(t)^{ \mathrm{H}} \bigr) \,\mathbf {M}_{\sigma } \,\mathbf {e}(t), $$
where E is the electric field strength, Ω is the spatial computation domain, the superscript H denotes the Hermitian, i.e., the complex conjugate transposed, and \(\mathbf {e}(t)=-\frac {{\mathrm {d}}}{{\mathrm {d}}t}\mathbf {a}(t)\) is the line-integrated discrete electric field. The Joule losses are plotted as well in Fig. 5. Figure 6 depicts the solution of (13), i.e., the coefficients \(\mathbf {w}(t_{1})\), exemplary for the current through the inductor \(i_{\mathrm{L}}\). As one can see, using the initial values (25), only the coefficient \(w_{j,0}\) corresponding to the zero-th basis function varies and the others stay constant. To quantify the accuracy and efficiency of the multirate PWM balance method, it is compared to conventional time discretization and to the MPDE approach with the original PWM basis functions. Different settings are considered: To analyze the performance of the conventional time discretization, the relative and absolute tolerance setting of the solver is changed, i.e., \(\mathrm{abstol}=\mathrm{reltol} \in [10^{-6}, 10^{-1}]\); For the case of the multirate PWM balance method and the MPDE approach with the original PWM basis functions, relative and absolute tolerances are fixed at \(\mathrm{abstol}=\mathrm{reltol}=10^{-7}\) and the number of basis functions \(N_{\mathrm {p}}\in \{1,\dots,10\}\) is changed. The accuracy is measured for the voltage output of the converter, i.e., the voltage at the capacitor. The relative \({\mathrm {L}^{2}}\) error is given by
$$ \epsilon (\mathrm{tol}, N_{\mathrm {p}}) = \frac{ \Vert v_{\mathrm{C,ref}}(t)-v_{ \mathrm{C}}^{\,h}(\mathrm{tol},N_{\mathrm {p}},t) \Vert _{{\mathrm {L}^{2}}(\varPsi )}}{ \Vert v_{ \mathrm{C,ref}}(t) \Vert _{{\mathrm {L}^{2}}(\varPsi )}}, $$
where \(v_{\mathrm{C,ref}}\) is the reference solution and \(v_{ \mathrm{C}}^{\,h}\) is the solution using the multirate PWM balance method and the MPDE approach with the original PWM basis functions. The norm is approximated using mid-point quadrature. Figure 7 shows the error plotted as a function of the solution time, i.e., the time that ode15s needs. For conventional time discretization the time for solving consists of the time that is needed to calculate consistent initial values and slopes after switching, and the actual time that ode15s needs. The time to calculate consistent initial values and slopes depends on the number of switching instants and is thus constant if the switching frequency or simulation interval does not change. It is given by approximately 16 seconds. The total time displayed in Fig. 7 is the sum of both contributions.
Multivariate voltage at the capacitor calculated using the multirate PWM balance method. The solution component corresponding to the original system of equations (1) is extracted along a diagonal and marked as a black curve
(top) Reference solution calculated using conventional adaptive time discretization compared to the solution obtained by the MPDE approach with \(N_{\mathrm {p},\mathrm {pwmbal}}=4\) PWM eigenfunctions. The relative \({\mathrm {L}^{2}}\) error of the current through the inductor similar to (27) is approximately \(3 \times 10^{-5}\). (bottom) Joule losses in the core material due to eddy currents
Coefficients \(w_{1,k}\) for the inductor current calculated by solving (13) with \(N_{\mathrm {p},\mathrm {pwmbal}}=4\). (top) real part. The coefficients \(w_{1,1}, \dots , w _{1,4}\) are approximately the same therefore they are hard to distinguish visually. (bottom) imaginary part
Error ϵ as defined in (27) over time for solving the systems of equations. The MPDE approach with PWM eigenfunctions (multirate PWM balance method) is considerably faster than the MPDE approach with the original PWM basis functions and the conventional time discretization
As one can see the MPDE approach with the original PWM basis functions is considerably slower than conventional time stepping. This is due to the fact that the already large systems of equations (1) (due to field-circuit coupling) are even further increased in size through the Galerkin approach. The stagnation of the error at 10−6 in Fig. 7 for values larger than \(N_{\mathrm {p}}=7\) is caused by the chosen accuracy of ode15s. Furthermore one can see that when adding another basis function the error does decrease with every second basis function. This was already observed in [5, 10]. For this reason the error for the PWM eigenfunctions is only plotted for \(N_{\mathrm {p},\mathrm {pwmbal}}\in\{1,2,4,6,8,10\}\). Since the systems of equations resulting from the multirate PWM balance method are decoupled, they can be solved efficiently in parallel. For each basis function \(g_{k}\) with \(k=0,\dots ,N_{\mathrm {p}}\), a complex-valued initial value problem of the form (16) has to be solved. The size of these systems of equations is the same as that of the original system of equations (1). However, the time for solving is considerably smaller since less time steps are necessary for the same solution accuracy. Note that due to the choice of the initial values (25) most coefficients in (13) for this numerical example do not change and only those corresponding to the zero-th basis function vary. This means that only the decoupled system of equations which corresponds to the zero-th basis function takes considerable computational effort to solve. In a parallel computing environment one would choose as many processor cores as basis functions (\(N_{\mathrm {p}}+1\)). The overall runtime is then determined only by the initial value problem that takes the longest to integrate. For this numerical example it is \(k=0\). The communication overhead between processors is not taken into account since it is highly implementation and machine dependent. The slightly decreasing time to solution when \(N_{\mathrm {p},\mathrm {pwmbal}}>1\) is owed to the fact that initial values according to (25) take more a-priori information into account which leads to smaller number of time steps and faster simulation. The overall accuracy of the method is problem-specific and always depends on both the tolerance for the solver and the number of basis functions. An a-priori determination of the number of basis functions and the solver tolerance is not yet available. An a-posteriori estimator can be constructed by increasing the number of basis functions and comparing the solutions. The resulting error is also related to the time stepping error.
The MPDE approach works also for nonlinear problems. However, similarly as for the harmonic balance case, the decoupling is not straightforward anymore. Furthermore the PWM basis functions and thus also the PWM eigenfunctions might not be able to represent the solution of problems with nonlinear elements [10]. If the amplitude of the ripples is small compared to the amplitude of the envelope, the particular efficient approach described in [9] can be applied. It uses only the slowly varying envelope to evaluate the nonlinearities. Although the assembly of the field model matrices for a new envelope cannot be parallelized, the matrices in (13) can still be decoupled and calculations to obtain the following time step can be run in parallel.
A new efficient technique was presented for field-circuit coupled models of DC-DC power converters, in which the switches are idealized and the filtering circuit is linear. The already existing MPDE technique with PWM basis functions splits the solution into fast varying and slowly varying parts. In this paper this method has been improved by introducing a new set of PMW basis functions which decouple the systems of equations similar as in the harmonic balance method. The new method, now called multirate PWM balance method, enables a parallel solution of all PWM modes resulting in a speed-up amounting to a factor 4 for the test example.
DOFs:
PWM:
pulse-width modulation
MPDE:
multirate partial differential equation
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This work is supported by the "Excellence Initiative" of German Federal and State Governments and the Graduate School CE at TU Darmstadt. The authors thank Johan Gyselinck for fruitful discussions. Further thanks go to Jonas Bundschuh and Erik Skär for their contribution to the first implementation of the PWM eigenfunctions.
Not yet available publicly. It is, however, planned to make the code, which is used to generate the results, publicly available in the near future.
No funding to report.
Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany
Andreas Pels, Herbert De Gersem & Sebastian Schöps
Institut für Teilchenbeschleunigung und Elektromagnetische Felder, Technische Universität Darmstadt, Darmstadt, Germany
Department of Electrical Engineering, EnergyVille, KU Leuven, Leuven, Belgium
Andreas Pels & Ruth V. Sabariego
Andreas Pels
Herbert De Gersem
Ruth V. Sabariego
Sebastian Schöps
All authors have jointly carried out the research and worked together on the manuscript. The numerical tests have been conducted by the first author. All authors read and approved the final manuscript.
Correspondence to Andreas Pels.
There are no competing interests to report.
Pels, A., De Gersem, H., Sabariego, R.V. et al. Multirate PWM balance method for the efficient field-circuit coupled simulation of power converters. J.Math.Industry 9, 8 (2019). https://doi.org/10.1186/s13362-019-0065-8
Linear circuits
DC-DC power conversion


Roy you never cease to amaze me on your collection.
Topic: What happened to Zeliard & Candyman ?
Re: What happened to Zeliard & Candyman ?
As of October of last year, Candyman was still working his job in Baton Rouge. I'm hoping he's doing ok, I've reached out to him on an old phone number, I'll let you know what I find.
Topic: Here is a strange rifle (at least to me) I was hoping someone could tell me about it. Thank you.
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My guess is a Kyber Pass, Frankenenfield. I agree horrible pic's, probably look even more like a hack job if the pic's were better.


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