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Unbalanced Equation

Abraham–Lorentz force

Book Blurb: Abraham–Lorentz Force Delve into the intricate world of electrodynamics with Abraham–Lorentz Force, a comprehensive exploration that spans over a century of scientific discovery. This book takes you on a journey from the foundational principles of classical electrodynamics, as established by Maxwell and Lorentz, through the early developments in radiation reaction and the formulation of the non-relativistic Abraham–Lorentz force. It then ventures into the realm of relativity with detailed analyses of the Abraham–Lorentz–Dirac equation and its modern extensions, including alternate formulations such as the Landau–Lifshitz approach. At its core, Abraham–Lorentz Force bridges the gap between theory and experiment. Readers will discover advanced theoretical perspectives, delve into experimental investigations that test these ideas, and explore how collective phenomena in plasmas and quantum theories converge to shape our understanding of self-interaction. The latter chapters address future directions and unresolved questions, challenging the reader to consider the classical–quantum transition, self-force problems in quantum gravity and string theory, and even the quest for a grand unified theory. Structured into twelve meticulously organized chapters, the book begins with: • Chapter 1: Foundations of Classical Electrodynamics – Laying the groundwork with Maxwell’s equations and the Lorentz force. • Chapter 2: Early Developments in Radiation Reaction – Tracing the pioneering work that first identified the self-interaction of accelerating charges. • Chapter 3: The Non-Relativistic Abraham–Lorentz Force – Analyzing the classical self-force in low-speed regimes. • Chapter 4: Relativistic Extensions and the Abraham–Lorentz–Dirac Equation – Extending the theory into the relativistic domain. • Chapter 5: Alternate Formulations and the Landau–Lifshitz Approach – Introducing pragmatic alternatives that avoid pathological predictions. • Chapter 6: Advanced Theoretical Perspectives – Exploring cutting-edge ideas that push the boundaries of current models. • Chapter 7: Experimental Investigations and Observations – Reviewing key experiments that validate and challenge theoretical predictions. • Chapter 8: Collective Phenomena in Plasmas – Examining how self-interaction affects the dynamics of complex plasma systems. • Chapter 9: Connections to Quantum Theories – Linking classical concepts to quantum electrodynamics and beyond. • Chapter 10: Future Directions and Unresolved Questions – Highlighting emerging research frontiers and ongoing challenges. • Chapter 11: Appendices – Providing essential mathematical identities, notational conventions, and historical documents. • Chapter 12: Analysis of References in Electrodynamics and Radiation Reaction – Evaluating the significance and impact of seminal works in the field. This book is an indispensable resource for PhD students, researchers, and professionals seeking to gain a deep, nuanced understanding of radiation reaction and self-interaction. It blends rigorous theory with practical insights, supported by extensive historical context and modern experimental evidence. With clear explanations, vivid analogies, and carefully structured content, Abraham–Lorentz Force not only encapsulates the evolution of electrodynamics but also illuminates the future directions of this dynamic field.
Andrew_Bardsley · 828 Views

Klas

**Topic: The Relationship Between Werewolves and Environmental Conservation** Ah, werewolves! Those majestic creatures that shake their furry selves on full moon nights, while humanity suspects that the real global crisis is not global warming, but rather the amount of screams echoing in the forests. If you think saving the planet is a difficult task, try adding a pack of werewolves to the equation and watch the magic happen! It's as if Gaia's army of good decided to use the "Help Thy Neighbor or Get Their Heads Roughly" methodology. Werewolves are, without a doubt, the pinnacle of evolution, if you consider that evolution got so bored that it decided to spice it up with fur, sharp claws and the ability to demand respect while biting the face of the guy who was cutting down the tree. We can compare them to those environmental activists who, after a good cup of organic coffee, put on a "Save the Turtle" t-shirt and think they're ready to face a tractor. The difference? The werewolves will probably snarl at the tractor and, with an immortal attack, transform the machinery into an elegant deer statuette. If you think condominium meetings are unbearable, try to imagine werewolves arguing about paper waste at their full moon celebration rituals. They gather with an intellectual tone, like a group of distinguished philosophers discussing whether Jesus’ sandals were vegan. “Oh, sure, the conscious use of recycled paper is important, but have you ever thought about the environmental impact of tearing a logger’s face off with your own teeth?” A debate of ideas that would make Aristotle cry tears of joy, while the earth trembles in terror. And let’s not forget the nostalgic side of the issue: these creatures are actually the answer you didn’t know you needed to your endangered plant problem. Want to give them a “don’t touch my forest” kind of protection? Is there anything more effective than a werewolf that will make you never look at the forest the same way again – let alone go into it to collect mushrooms? Why bother with all this “#LoveMySpoiledPets” hashtagging when you can just adopt a werewolf and laugh at the ninjas of destruction trying to threaten your pack? In conclusion, the real lesson we can learn from werewolves is that when it comes to the survival of the planet, it’s better to risk a few sharp teeth and an extra dose of anger than to sit on the couch watching a documentary about how turtles are having it harder than a marathon runner in an obstacle course. So the next time you hear a howl in the moonlight, remember: it’s just a werewolf concerned about the environment, wondering where the last tree he loved to mark his territory went! Which, by the way, is a fantastic metaphor for our fight against planetary destruction: that, just like a werewolf, we must be fierce, hairy, and willing to rip the face off anyone who dares to threaten the living Earth!
SuokTV · 2.1K Views

Gluttonous System Holder

Thousands of years passed since humanity existed. Achieving societal evolutions through modern technologies made human capabilities advance further to the extent that humans started inhabiting the nearest habitable planet Mars, and even go beyond residing the habitable satellites, while extracting usable minerals and materials from other celestial bodies in the entire solar system they've known for centuries. There existed unbalanced treatment between poor and rich that should have been resolved throughout the decades but greed took over the social structure after the founding new Earth Era executives died and succeeded with unworthy executive candidates. ---- While rich people enjoy living the life beyond fullest, the poor were scattered throughout the forsaken realms of the Earth, and got to live modestly while enduring the scarcity of supplies needed, neither the human organizations nor rich considered these forsaken inhabitants as human. One starry evening on one of the Earth's forsaken realm - Hellish Pit, there a lone forsaken inhabitant got abandoned by his adult companions. He's Neil, just turned 5 years old the day he was left alone in one of the considerably deserted island among the lands known as Forsaken Realms. Aside from Technological advancements, humans did evolved a step further when it comes to capabilities. Rich people were amongst the talented individuals, possessing their innate evolutionary talents, aided by technology they can afford and prestigious schools to attend, they enhanced these talents well, on the other hand, amongst poor, there were also some promising people and hence the scattered forsaken guilds often invest money on procuring aiding technology and books to hand over with these people while those devoid of luck amongst themselves got abandoned in places that forsaken realm inhabitants wouldn't even dare to think about residing. It was due to their quite irrationally rational thinking, - building their forsaken society made of strong people bound to yield greater good than keeping those untalented individuals. Aside from the lack of technology, humans still need to think about their basic necessities after all, such as food and water, though forsaken people adapted well enough in their environment, this isn't something that can be taken lightly when it comes to food and water supply. The strong must survive - says the founding and current leaders in the forsaken realm. Neil, a innocent, loving, intellectual child that just got 5 years old was abandoned after his father who was the head of Resistor Forsaken Realm Organization - one of the big organizations existed in the forsaken region, got assassinated, while his mother died after giving him birth. With his mom long gone, and his father's sudden death, there was no one to take care of him nor the high-ranking executives of organization wants too. Discarding the successor of the organization is the best way to relieve their greed after all, all these high executives have to do was fake the child's death, and the lower ranking people can't do anything about the situation than to be bound by the greedy new highest executives of the most respected and fair organization amongst the running company in the land of desolated people. Neil the unsuspecting child who lacks the protection from dangers of the world in a such a young age got himself shut from things he deserves. Now being left alone, scared, and hungry, his adventure begins.
Lrzn · 6.6K Views

The Original Character Lives in the Fanfic World

There was a popular comic that captured the hearts of readers not because of its plot, but rather the bromance between the two protagonists, a crown prince and a duke. Their friendship & mutual trust led fans to ship them endlessly, with countless fanfiction stories ranging from dating to marriage or even incorporating omegaverse settings. One particular m-preg fanfic novel became extremely popular among fans, where the previously cold duke becomes pregnant. But the popularity of both the original comic and this novel caused everything to become unbalanced, until something strange happened - these works of fiction turn into real worlds that collided, creating an error that connected them together. In the world of the comic: Carlton from the fanfic world gazed up at his husband with longing eyes. "Husband..." He pouted, "Why don't you kiss me today?" Alaric from the comic world recoiled slightly and goosebumps broke out over his skin as he moved away. "Please don't come close to me..." He said tersely. Meanwhile, in another world: Alaric from the fanfic world, pulled his beloved Carlton into a warm embrace and peppered kisses on his cheeks. "Darling, are you mad at me?" Alaric asked affectionately. "It's okay, you're still cute." He leaned down to whisper into his ear before continuing. "But don't forget to comfort all our children, they think you're mad at them." Suddenly, seven children barged into the room and called out to their fathers. "Father, Daddy!" they exclaimed. Carlton's frozen expression spoke volumes about his state of mind as he tried to process what was happening. His murderous gaze fixed on Alaric as he muttered through gritted teeth. "Whose children do you say they are....?"
callciel_rin · 14.6K Views

The Billionaire's Heart:A Deadly Triangle

In the glittering world of wealth and power, two ambitious women, Amara Winston and Evelyn Hart, find themselves drawn to the enigmatic Lucas Rayner, a self-made billionaire with a mysterious past. As heirs to rival empires, Amara and Evelyn have spent their lives competing for dominance in society and business, but their rivalry takes a dangerous turn when love enters the equation. Amara is calculated and poised, embodying the legacy of her traditional, old-money family. Evelyn, fiery and unpredictable, represents the bold innovations of a new generation. Both women are determined to secure Lucas's attention—not just for personal gain, but for the undeniable connection they each feel with him. Lucas, however, is not an ordinary man. Beneath his charming demeanor lies a complex web of secrets and motives. While Amara and Evelyn vie for his heart, Lucas quietly orchestrates a game of his own, testing their limits and exposing vulnerabilities they never knew they had. As business deals intertwine with personal desires, alliances are forged, and betrayals become inevitable. The stakes escalate when long-buried family secrets emerge, threatening to unravel the foundations of the Winston and Hart empires. Lucas becomes the key to salvation—or destruction—for both families. In a world where every move is calculated, every word is weighed, and every relationship has a price, Amara, Evelyn, and Lucas must navigate the delicate balance between love, ambition, and survival. But in the end, only one question remains: will love triumph, or will the game of power consume them all?
royalSs · 6.2K Views

Eye of the Needle: Into the Reikai

Faith, fear, and fury. The strongest, most inalienable things that make us human. While the people of the world learn and grow, they shed feeling and emotion as time passes. Much like how matter cannot truly be destroyed, the energies of these sentiments never dissipates. Instead, it feeds beings born of all types of things, from ancient cultural followings to widespread societal discourse. In turn, these beings give back to the world--for better or worse. After the traumatic incident of his father's death, young DeMain is thrust into a world of turmoil and a hidden people right under the world's nose. As he harnesses a rare and unique ability gifted to him in exchange for his suffering, his view of the world unravels as he converges with others given the gift of Witchblood, an ability to see and interact with spirits. This book will take on its narrative based on the first-person views of three separate protagonists. I will remind those reading that 'protagonist' does not equate to 'hero' in all cases. A forewarning: This story includes many heavy themes and I felt the need to write them with the reality of how they happen. As such, be cautious. This book contains mentions of sexual assault, murder, violence, substance abuse, and overall conflict. There are also quite a varied amount of scenes with some 'gross' aspects to them. Though I imagine this would only affect those with vivid imaginations, you deserve to be warned regardless. Updates will done be once weekly if not more. (Things are subject to edits and changes!)
DystopianSmile · 18.8K Views

The Fractured Realm

Eliar Vayne was a man who thrived on logic, a mathematician devoted to unraveling the universe’s most complex mysteries. But when an experiment in his lab goes catastrophically wrong, he finds himself thrust into a shattered, alien world—a place ruled by chaos and cruelty, where survival is the only law. In this desolate realm of jagged landscapes and crimson skies, Eliar is no longer bound by the rules of his old life. Here, power is drawn from the raw energy pulsing through the world itself—a chaotic force that bends to those strong enough to command it. For Eliar, logic is his only weapon. With his understanding of patterns and equations, he begins to shape the energy into spells unlike anything this world has seen. But the world he’s been thrown into is not merciful. Predators stalk the shadows, rival survivors would sooner kill than trust, and the land itself seems alive with malevolent intent. Eliar must adapt quickly, forging alliances where he can and outwitting enemies who see his intellect as weakness. Every step forward is a battle, every mistake a potential death sentence. As Eliar navigates this unforgiving world, he uncovers traces of an ancient civilization—a people who once mastered the same energy he now wields. Their downfall holds the key to understanding this broken realm, and perhaps, to Eliar’s survival. But the deeper he delves into the world’s secrets, the more he realizes the truth: this world has no intention of letting him leave unscathed. Driven by the faint hope of carving out a peaceful existence, Eliar must endure relentless trials and confront the darkness within himself. In a world without mercy, only those who embrace the chaos will survive.
Ben_Dover69 · 8.3K Views

An Ordinary Complex

_ _ _ _ MXFXF relationship. Please read the note. Please add it to the collection then and support me. All feedback will be appreciated Perhaps everyone was right, but Lisa Grace was cursed. How else would you explain what happened to her life and her dream of living an Ordinary Life? ——— ‘This will not work out, so we should break up now. It’s not you, it’s me! I recently found my soul mate and want to be with them.” Lisa was not shocked when her boyfriend told her this. She did not even have enough energy to be angry or demand answers. Perhaps she would have said something if this was the first time this happened. However, after being broken up for the 24th time, Lisa had no hope of ever having a meaningful relationship again. After all, Lisa was an ordinary girl with an extraordinary rumor - if you dated her, you would find your soul mate. So, when a stranger approached Lisa with red eyes, a charming smile, and a beautiful face, she expected it to be a quick relationship for her. But little did she know she was stepping into a world she could never escape. Would the flash of gold she saved become her salvation? Or would that beautiful temptation make her forget her world? …… “All I ever wanted was an ordinary life with someone who cared! It would have made my mother’s neglect and my father’s absence much easier for me to bear!” Lisa wanted this in her life—to be ordinary and never worry about her place in the world. However, just because ‘SHE’ wanted to be left alone did not mean that the ‘World’ would let her be alone. She had made these two fall for her, and now she would be stuck with a vampire’s obsession and a werewolf’s possessiveness. ______ This story will have a straight pairing as well as Yuri and will have abo themes as well as fantasy themes. Female Alphas are Futas. If it's not your cup of tea, leave before you enter. MXFXF relationship, age gap, and unbalanced relationships. Please read the note, add it to the collection, and support me. All feedback will be appreciated. Leave a lot of feedback for me.
Holy_mackrel · 144.2K Views

The Nerd Teacher I Love

" Lucian, what are you doing?"... " Shhhh!...". " Lucian, what- ...". " Who has the guts to harass the love of my life?. I will make them pay with their blood...". Lucian said tucking his loose hair into a hair strand. "I.. AM.. NOT.. THE.. LOVE ... OF ...YOUR...LIFE...". " Dare to say that again, and I swear a God, in no time, you will see your self under me, and I make sure you won't rest until the morning, after I might have left you exhausted". He is the teacher with glasses... He is the boy with tattoos and piercings... Emerson Pearl College 's brightest and youngest professor, Michael Temple , a brain wizard whom could solve and balance any kind of chemical equation, just by looking at them. He is the real definition of a saint cute nerd guy that loves solitude and appreciates tranquility. Born and raised in a strict Roman Catholic home, and he's father a Cathceist was groomed to live a perfect life, get married and have kids, but not until his peaceful life gets disturbed as soon as Vernice's baddest boy, Lucian Peterside, gets admission to study in Emerson Pearl College... Lucian Peterside- a mistake of one night, and everyone's nightmare as well as fantasy boyfriend. Strong, hot and sexy, with tattoos and piercings all over him, with a dangerous secret lurking behind him... Micheal Promises himself that he would avoid trouble , by staying far away from him, even during classes, but unknown to him, he gains Lucian's attention, which turns out to be a battle, battle of family beliefs, love and acceptance. Will Micheal accept Peter?.. inspite of his family background?. And for whom Lucian is?..
Blessing_Ezeh_7290 · 1K Views

Roost of the Palace

In a land of long ago, the soils were untainted by the cruelty of war. Kingdom's stayed in peace, every monarch kept their feet up as the everyday within their land flowed like the fresh waters. Kingdom's that consist of humans, beings that all had their own trade, each kingdom providing unique and exotic goods. But one stuck out, a Kingdom that almost fully exists within the mouth of the large volcano of Vallendrconis. The unpredictable aggression of nature was tamed by the magic that this kingdom held. That magic being far greater than any mage could wish to have. The gift of the ability to shift their weaker and non-magical bodies into that of the graceful and powerful dragons. The kingdom that had fully built on those who weld a dragon morf. The dragon's built their kingdom with the natural magic, the elements. Taming the molten larvar and building a grand Palace within it's mouth. With their power they've built a peace over all kingdom's, their own kingdom acting more as a council. This peace was not ment to last. Within the ancient times, a tradidy struck, a poisoned arrow had hit its target. As the poison took the life of The Queen of Montes, so did the lives of many soldiers. The poison of such a cruel and twisted power could only be brewed from the volcanic flowers of the Draconis kingdom's. The dragon morf kingdom. The King of Montes declared a war that outnumbered the dragons. Banishing them underground where they're cursed to live in the deepest depths like monsters. A gift fell on the Kingdom, a prophecy, declaring "When the war has been scorched from history, when dragon's and human's have grown. A Queen will fight for the blade, who will set foot on the grand Palace again. A King will rebirth their grace and together their new monarch and heritage will forge the blade into peace. Birthing the new empire and a new dawn of time will be born". Nearly over two centuries had past since the great tradidy. The surface having been wiped with any evidence of the dragon morf's existence. And the once great kingdom became a muffled myth, turning into the villians of the old fairy tales. Now the four kingdom's rule over their own land, peace unbalanced and any alliance so easily lost. Princess Shir of the, newer and largest, kingdom of Vallendrconis, was raised. This Princess had been set up to marry the Prince of Montes, the oldest kingdom. Princess Shir knew of Prince Rknom, hearing the tales of how he defended his kingdom against a stampede of trolls, fighting the foul beasts off and protecting his kingdom. Princess Shir also knew the delicate but also unstable relationship between the Vallendrconis kingdom and the Montes kingdom. The two having only recently left a war on a peace treaty, now seeking an alliance. That's where their marriage came in, Princess Shir knows the importance of this ordeal but deep within her heart she knows she's ment for something much greater. She knows that becoming some lonely Queen to a warrior King was not the path set out for her but could she abandon her duties on a hunch? Or will she have to forfill her duties and marry this Prince for the sake of her kingdom's alliance? Further down into the earth, a fallen kingdom scrambled like rats. The once proud and noble kingdom having lost any grace they had after being banished. Prince Eoviet finding struggling into feeding himself let alone the very few left of his people. In a last attempt he used the old tunnels up before his now twisted and scaleless snout poked into the open air. The first for his kind to see the open world in over two centuries. Now under the mercy of the Princess, he had found himself digging around for any sign of hope for his people. To find the last evidence of his grace within the volcano.
Tahliz · 8K Views
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