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Flow

Flow is a term with multiple meanings across various disciplines. In psychology, it refers to a state of optimal experience characterized by complete immersion in an activity, intense concentration, loss of self-consciousness, distorted time perception, and intrinsic enjoyment, often resulting from a balance between task challenges and personal skills. This psychological concept, coined by Mihaly Csikszentmihalyi in his 1975 book Beyond Boredom and Anxiety, has been extensively studied and applied in areas like education, sports, and work.^[1]^[2] The term "flow" also appears in natural sciences, such as physics and fluid dynamics where it describes the motion of fluids, and in biology and physiology related to physiological processes. In social sciences, beyond psychology, it is used in economics and business to denote the movement of resources or information. Technology contexts include computing and information systems (e.g., workflow or data flow) and engineering and manufacturing (e.g., production flow). Additionally, "flow" features in arts and media, including film, television, music, and literature, as well as in brands, products, sports, and recreation. Detailed discussions of these uses are covered in subsequent sections. Csikszentmihalyi's research identified key elements of psychological flow, such as clear goals and immediate feedback, contributing to its autotelic quality. His 1990 book Flow: The Psychology of Optimal Experience popularized the idea based on studies of diverse professionals experiencing peak engagement.^[3] The concept influences broader fields, with neuroscientific evidence linking it to altered brain activity, including reduced self-referential processing and enhanced reward mechanisms.^[4] Achieving flow involves aligning challenges with skills to prevent boredom or anxiety.^[5]

Natural Sciences

Physics and Fluid Dynamics

In physics and fluid dynamics, flow refers to the continuous deformation of a fluid—a substance that deforms indefinitely under applied shear stress without a total loss of volume—resulting in the motion of fluid particles relative to a solid boundary or within the fluid itself.^[6] This deformation occurs as fluids, such as liquids and gases, respond to forces like pressure gradients, gravity, or viscosity, enabling the transport of mass, momentum, and energy. Fluids are modeled as continua in this context, assuming molecular-scale effects are negligible over macroscopic distances.^[7] Flows are classified as steady or unsteady based on temporal variations in fluid properties. In steady flow, the velocity, pressure, and density at any fixed point remain constant over time, allowing simplification in analysis as the flow pattern does not evolve.^[8] Unsteady flow, by contrast, involves time-dependent changes in these properties, such as in pulsating or accelerating flows, which complicate predictions and require accounting for transient effects.^[9] A central distinction in fluid dynamics is between laminar and turbulent flow regimes, which dictate the nature of fluid motion. Laminar flow features smooth, orderly layers of fluid sliding past one another with minimal mixing, prevalent at low velocities where viscous forces dominate. Turbulent flow, however, is characterized by chaotic, irregular eddies and vortices that enhance mixing and momentum transfer, occurring when inertial forces overpower viscous effects. The transition between these regimes is predicted by the Reynolds number, a dimensionless quantity defined as

Re = \frac{\rho v d}{\mu},

where \rho is the fluid density, v is the characteristic velocity, d is a characteristic length (e.g., pipe diameter), and \mu is the dynamic viscosity. Typically, Re < 2000 indicates laminar flow, Re > 4000 suggests turbulence, and intermediate values mark a transitional zone.^[10] Bernoulli's principle provides insight into pressure-velocity relationships in inviscid, incompressible flows along a streamline. It states that the total mechanical energy per unit volume remains constant, expressed as

P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant},

where P is static pressure, \frac{1}{2} \rho v^2 is dynamic pressure, and \rho g h is hydrostatic pressure (with g as gravitational acceleration and h as height). This equation, derived from conservation of energy, implies that an increase in fluid speed corresponds to a decrease in pressure, assuming negligible viscous losses and steady flow. It applies to ideal fluids but offers approximate insights for real scenarios when friction is minor. These principles manifest in diverse natural and applied contexts. In aerodynamics, airflow over an aircraft wing accelerates atop the curved surface, reducing pressure and generating lift via Bernoulli's principle, enabling sustained flight.^[11] River currents often exhibit turbulent flow due to high Reynolds numbers from large scales and velocities, promoting sediment transport and channel erosion through eddy-induced mixing.^[12] Volcanic lava flows, as highly viscous non-Newtonian fluids, demonstrate slow, unsteady motion governed by gravity and rheology, with turbulence limited by high viscosity but channeling heat and material over landscapes.^[13] The foundations of modern fluid dynamics trace to key historical contributions. Daniel Bernoulli introduced the principle in his 1738 treatise Hydrodynamica, applying energy conservation to fluid motion and deriving the pressure-velocity relation for steady, inviscid flows.^[14] Osborne Reynolds advanced understanding of flow regimes in 1883 through experiments visualizing transitions in pipe flow, establishing the Reynolds number as a predictor of laminar-to-turbulent shifts and influencing turbulence studies.^[10] These works laid the groundwork for Euler's later Navier-Stokes equations, unifying theoretical and experimental approaches.^[15]

Biology and Physiology

In biological systems, flow is fundamental to the transport of nutrients, oxygen, waste, and signaling molecules, enabling homeostasis and survival across diverse organisms. In animals, the circulatory system exemplifies this through blood flow, where the heart acts as a central pump to propel oxygenated blood via arteries and deoxygenated blood via veins, while vascular resistance modulates distribution to tissues. This process relies on laminar flow principles, with blood vessels approximating tubes where flow rate is governed by Poiseuille's law: Q = \frac{\pi r^4 \Delta P}{8 \mu L}, where Q represents the volumetric flow rate, r the vessel radius, \Delta P the pressure difference, \mu the blood viscosity, and L the vessel length; the fourth-power dependence on radius underscores how small changes in vessel diameter profoundly influence flow efficiency.^[16]^[17] In humans, the average cardiac output at rest is approximately 5 liters per minute, reflecting the balance between heart rate, stroke volume, and systemic demands. Disruptions to this flow, such as thrombosis where a blood clot obstructs vessels, can severely impair perfusion, leading to ischemic strokes by blocking cerebral arteries and causing tissue damage.^[18]^[19] The lymphatic system complements circulation by managing interstitial fluid flow, preventing accumulation that could cause edema. Lymph fluid, derived from plasma leakage, moves unidirectionally through lymphatic vessels via extrinsic mechanisms like skeletal muscle contractions during movement and intrinsic pumping from smooth muscle in vessel walls, aided by one-way valves that counteract gravity and pressure gradients. This peristaltic-like action ensures efficient return of lymph to the bloodstream at the subclavian veins, maintaining fluid balance and immune surveillance; failure in these mechanisms contributes to lymphedema by allowing fluid buildup in tissues.^[20]^[21] In plants, vascular tissues facilitate analogous flow processes tailored to sessile lifestyles. Xylem conducts water and minerals upward from roots to shoots, driven by transpiration pull: evaporation from leaf mesophyll cells creates negative pressure (tension) in xylem vessels, drawing water column via cohesion and adhesion forces against gravity, often exceeding 100 meters in tall trees. Phloem, conversely, transports sugars and nutrients bidirectionally, explained by the pressure-flow hypothesis where osmotic gradients at source tissues (e.g., photosynthesizing leaves) load solutes into sieve tubes, generating turgor pressure that propels sap toward sinks like roots or fruits, with unloading at low-pressure sites completing the cycle.^[22]^[23] Evolutionary adaptations have optimized flow efficiency across species, reflecting environmental pressures. In fish, gill perfusion exemplifies this through countercurrent exchange in lamellae, where blood flows opposite to water across thin epithelia, maximizing oxygen diffusion gradients and achieving up to 80% extraction efficiency from ambient water— an adaptation honed over 400 million years for aquatic respiration. Such innovations, from closed circulatory loops in vertebrates to specialized vascular tracheids in plants, highlight flow's role in enabling diverse physiologies while minimizing energy costs.^[24]

Psychology

In psychology, flow refers to a mental state of optimal experience characterized by complete absorption in an activity, where action and awareness merge seamlessly, self-consciousness diminishes, and the sense of time becomes distorted.^[25] This concept was first articulated by Mihaly Csikszentmihalyi in his 1975 book Beyond Boredom and Anxiety, based on interviews with artists, athletes, and professionals who described moments of intense focus and intrinsic reward during challenging tasks.^[5] The core components of flow include clear goals that provide direction, immediate feedback on performance to sustain engagement, and a balance between the perceived challenges of the task and the individual's skills.^[26] This balance is illustrated by the channel model, in which flow emerges when challenges match skills; mismatches lead to anxiety if challenges exceed skills or boredom if skills surpass challenges.^[27] Flow experiences are often measured using the Experience Sampling Method (ESM), which involves participants reporting their mental states via prompts throughout daily life, revealing higher rates of positive affect and engagement during flow compared to other states.^[28] The benefits of flow include enhanced creativity, as individuals produce novel ideas with reduced self-criticism; increased productivity through sustained concentration; and improved well-being, with reports of greater life satisfaction and lower stress.^[26] Applications span education, where flow fosters intrinsic motivation and deeper learning by aligning tasks with student abilities; sports, promoting peak performance through focused immersion during competition; and therapy within positive psychology interventions, helping clients cultivate flow to build resilience and emotional regulation.^[29]^[30]^[31] Key research milestones include Csikszentmihalyi's 1990 book Flow: The Psychology of Optimal Experience, which synthesized decades of studies to popularize the theory and link it to broader human fulfillment.^[26] Subsequent work identified neural correlates, such as transient hypofrontality—a temporary reduction in prefrontal cortex activity that minimizes executive interference and enables effortless action.^[32] This draws a metaphorical parallel to smooth, unimpeded fluid motion in physics, where obstacles are minimized for optimal progression.^[33] Recent research from 2020 to 2025 has further developed flow theory, including meta-analyses showing that personality traits like openness and conscientiousness predict greater flow proneness, and scoping reviews highlighting how natural and built environments enhance flow experiences.^[34]^[35]

Economics and Business

In economics and business, flow refers to the dynamic movement of resources, money, and information within systems and organizations, enabling the assessment of efficiency, stability, and value creation. Cash flow, a core metric, represents the net amount of cash generated or received by a business over a specific period, providing insights into its liquidity and operational health. The cash flow statement categorizes these movements into three primary components: operating activities, which cover cash from core business operations like sales and payments to suppliers; investing activities, involving cash used for or generated from asset acquisitions and sales; and financing activities, encompassing cash exchanges related to debt, equity, and dividends.^[36]^[37] A key derivative is free cash flow (FCF), which measures the cash available after accounting for necessary capital investments, calculated as:

FCF = \text{[operating cash flow](/page/Operating_cash_flow)} - \text{capital expenditures}

This formula highlights a firm's capacity to pursue growth, pay dividends, or reduce debt without external financing.^[38] In supply chains, flow encompasses the interconnected streams of materials (physical goods moving from suppliers to customers), information (data on orders, inventory, and forecasts), and finances (payments and credit terms across tiers). Disruptions in these flows can amplify inefficiencies, as seen in the bullwhip effect, where minor variations in consumer demand lead to progressively larger fluctuations in orders and inventory upstream, increasing costs and stockouts. This phenomenon, analyzed through demand signal processing, order batching, rationing, and price fluctuations, underscores the need for coordinated information sharing to stabilize supply chain dynamics.^[39] Workflow in business denotes the sequential orchestration of tasks and decisions to execute processes efficiently, often visualized through standardized notations like Business Process Model and Notation (BPMN). BPMN provides a graphical framework for diagramming end-to-end processes, including events, tasks, gateways, and message flows, facilitating analysis and automation in organizational settings.^[40] Key conceptual tools for optimizing these flows include value stream mapping, a lean methodology technique that charts the entire sequence of activities—from raw materials to customer delivery—to pinpoint waste such as excess inventory, waiting times, or overproduction, thereby streamlining resource circulation. Complementing this is input-output analysis, pioneered by Wassily Leontief in 1936, which models economic circulation as a matrix of inter-industry flows, quantifying how outputs from one sector become inputs for others to evaluate multipliers, dependencies, and policy impacts.^[41]^[42] The 2008 financial crisis exemplified vulnerabilities in financial flows, where liquidity disruptions—marked by frozen interbank lending and asset devaluation—severely impaired credit provision, leading to widespread economic contraction and highlighting the systemic risks of interrupted cash and capital circulations. More recently, the COVID-19 pandemic (2020–2022) highlighted vulnerabilities in global supply chains, with lockdowns causing widespread disruptions in material and information flows, exacerbating the bullwhip effect and leading to shortages; as of 2025, ongoing geopolitical tensions and climate events continue to pose similar risks.^[43]^[44]^[45]

Technology

Computing and Information Systems

In computing and information systems, flow concepts underpin various paradigms for program execution, data processing, and network optimization. Historically, one of the earliest contributions was Flow-Matic, developed by Grace Hopper in the 1950s at Remington Rand for the UNIVAC I and II computers, which introduced an English-like data-processing compiler that influenced the design of COBOL by emphasizing readable, business-oriented instructions.^[46] This laid groundwork for structured programming approaches that manage execution sequences. Control flow refers to the order in which individual statements, instructions, or function calls are executed or evaluated within a program, typically following a sequential path but altered by constructs such as branching (e.g., if-else statements) and loops (e.g., for or while iterations).^[47] These mechanisms dictate how a program's logic progresses, enabling conditional decisions and repetitions to handle complex tasks efficiently. Control flow is often visualized using flowcharts, which employ standardized symbols for operations, decisions, and data movement; the ANSI/ISO 5807:1985 standard defines these conventions for program flowcharts, system flowcharts, and related diagrams to ensure clarity in documentation.^[48] In contrast, the data flow paradigm models programs as sequences of transformations on data streams, where execution is driven by the availability of data rather than explicit control sequences, promoting parallelism and modularity.^[49] A foundational model is Kahn process networks, introduced by Gilles Kahn in 1974, which describe concurrent processes communicating via unbounded FIFO queues in a deterministic manner, serving as a theoretical basis for dataflow architectures that enable efficient parallel computing without race conditions.^[50] Network flow, rooted in graph theory, addresses optimization problems in directed graphs with capacity constraints on edges. The maximum flow problem seeks the greatest possible flow from a source to a sink while respecting these limits, solved by the Ford-Fulkerson algorithm, which iteratively finds augmenting paths to incrementally increase flow until no more exist.^[51] This approach, with applications in traffic routing and resource allocation, ensures optimality via the max-flow min-cut theorem, where the maximum flow equals the minimum capacity of a source-sink cut. Workflow systems extend these ideas to automate task orchestration in information systems, defining sequences of dependent operations as directed acyclic graphs (DAGs). Apache Airflow, an open-source platform, enables programmatic authoring, scheduling, and monitoring of such workflows using Python, integrating with business process management (BPM) tools for scalable data pipeline execution.^[52] Modern reactive programming paradigms, exemplified by RxJS—a JavaScript library for composing asynchronous and event-based programs using observables—build on data flow principles to handle streams of data reactively, facilitating responsive user interfaces and real-time processing.^[53]

Engineering and Manufacturing

In engineering and manufacturing, flow principles are applied to optimize the movement of materials, fluids, and energy within designed systems, ensuring efficiency in production processes. Process flow diagrams (PFDs) serve as essential tools in chemical engineering for visualizing the sequence of operations in plants, depicting streams of materials and energy along with equipment and conditions.^[54] These diagrams facilitate the design and analysis of complex systems by illustrating the path of components from raw materials to products. For incompressible fluids in such systems, the continuity equation governs mass conservation, expressed as A_1 v_1 = A_2 v_2, where A represents cross-sectional area and v velocity, enabling engineers to predict velocity changes in pipes or channels.^[55] Material flow analysis in supply chain engineering quantifies the movement of goods to minimize waste and enhance logistics, often integrating technologies like radio-frequency identification (RFID) for real-time tracking of inventory across facilities.^[56] Just-in-time (JIT) systems, a cornerstone of lean manufacturing, synchronize material delivery to production needs, reducing inventory holding costs by ensuring components arrive precisely when required.^[57] RFID enhances JIT by providing automated visibility into material locations, allowing for dynamic adjustments in flow to avoid bottlenecks.^[58] Energy flow in thermodynamic systems underpins heat transfer and fluid power applications, such as hydraulic systems where actuators convert fluid pressure into mechanical work. In these setups, the volumetric flow rate is given by Q = A v, linking fluid velocity to system performance in powering machinery like presses or lifts.^[55] This equation, derived from continuity principles, helps engineers size pumps and lines to maintain efficient energy transmission while minimizing losses.^[59] Pipeline design relies on Darcy's law to model fluid flow through porous media, such as in oil reservoirs or filtration systems, with the equation Q = -\frac{k A \Delta P}{\mu L}, where k is permeability, \Delta P pressure drop, \mu viscosity, A area, and L length. This formulation allows for calculating throughput in subsurface transport, informing the layout of extraction and distribution networks. In automotive manufacturing, assembly line balancing optimizes the flow of tasks and parts, exemplified by Henry Ford's 1913 implementation at the Highland Park plant, which reduced Model T production time from over 12 hours to about 93 minutes by sequencing operations along a moving conveyor.^[60] Post-2010 innovations in additive manufacturing have enabled the 3D printing of intricate flow channels, allowing customized designs for microfluidics in heat exchangers or lab-on-a-chip devices that traditional machining could not achieve. These advancements facilitate rapid prototyping of complex geometries, improving fluid distribution in compact systems for biomedical and chemical applications.^[61] Computational simulations briefly aid in refining these engineered flows by predicting performance prior to fabrication.

Arts and Media

Film and Television

Flow (2024) is a Latvian animated adventure film written, directed, and produced by Gints Zilbalodis, who also handled animation using Blender software.^[62] The film follows a solitary black cat that, after its home is destroyed by a massive flood in a post-human world, joins a diverse group of animals—including a capybara, lemur, dog, and secretarybird—on a small boat to navigate flooded landscapes and search for dry land.^[63] Without dialogue, the story emphasizes themes of environmental disruption, adaptation, and interspecies cooperation amid rising waters, drawing parallels to climate change impacts on natural flows.^[64] Premiering in the Un Certain Regard section at the 2024 Cannes Film Festival, it received critical acclaim for its minimalist narrative and stunning visuals, earning a 97% approval rating on Rotten Tomatoes.^[65] Flow won the Jury Prize at Annecy International Animation Film Festival, the Golden Globe for Best Animated Feature Film, and the Academy Award for Best Animated Feature at the 97th Oscars, marking Latvia's first win in that category.^[66]^[67] Zilbalodis's earlier animated short Aqua (2012), created when he was 17, similarly explores themes of survival in a flooded world, centering on a cat adapting to an aquatic environment after awakening surrounded by water.^[68] This hand-drawn and 3D hybrid work, lasting about 7 minutes, foreshadows the environmental and animal-centric motifs in Flow, though it received recognition through online platforms and festivals rather than major awards like Annecy.^[69]^[70] In television, the concept of flow appears metaphorically in series like The OA (2016–2019), a Netflix drama where interdimensional "movements" represent fluid transitions between realities, blending dance-like sequences with narrative progression to evoke a sense of seamless, otherworldly flow. Documentaries on physical flow in fluid dynamics include BBC Four's The Secret Life of Waves (2011), presented by David Malone, which examines ocean wave formation, propagation, and behavior, revealing how waves carry energy rather than water itself and influence coastal ecosystems.^[71] The 58-minute film uses slow-motion footage and scientific explanations to illustrate wave interference, rogue waves, and their role in natural flow patterns.^[72] Among other audiovisual works, Flow State (2012), a production by Warren Miller Entertainment, delves into the psychological dimension of achieving a "flow state"—a heightened focus where athletes merge with their environment during extreme sports.^[73] Narrated by Jonny Moseley, the film features segments on skiing and snowboarding in remote locations like Alaska and Japan, exploring how this mental immersion enhances performance and alters time perception, with brief extensions to analogous activities like big-wave surfing for broader insights into peak human experience.^[73]

Music and Literature

In music, "flow" refers to the rhythmic and articulative delivery of lyrics or phrases, particularly in genres like hip-hop and rap, where it encompasses timing, cadence, and syllable placement to create seamless momentum over beats.^[74] This technique allows performers to layer complex rhyme schemes and vocal inflections, enhancing emotional impact and listener engagement. For instance, Eminem's intricate flows, characterized by rapid shifts in pitch and rhythm, exemplify how prosodic variations can heighten lyrical density and narrative drive in tracks like those on his album The Marshall Mathers LP.^[75] In jazz improvisation, flow manifests as a continuous, intuitive stream of melodic and harmonic ideas, where musicians maintain rhythmic coherence amid spontaneous variations, as seen in the fluid solos of artists like John Coltrane, who emphasized unbroken phrasing to evoke organic progression.^[76] Specific works highlight flow's thematic and structural role in music. The song "Go with the Flow" by Queens of the Stone Age, from their 2002 album Songs for the Deaf, uses driving guitar riffs and Josh Homme's steady vocal rhythm to metaphorically capture effortless adaptation and release, peaking at number one on the Billboard Mainstream Rock Tracks chart and influencing alternative rock's rhythmic ethos.^[77]) In beatboxing, flow denotes the seamless integration of percussive sounds and basslines into rhythmic patterns, enabling performers to mimic instrumental tracks vocally while sustaining momentum, a skill central to human beatboxers like those in the Human Beatbox community who prioritize timing and layering for dynamic performances.^[78] In literature, flow pertains to narrative rhythm and pacing, guiding the reader's experience through sentence structure, repetition, and syntactic fluidity to mimic thought processes or emotional currents. James Joyce's Ulysses (1922) pioneered this through stream-of-consciousness techniques, particularly in episodes like "Penelope," where unpunctuated prose creates a relentless, associative drift that immerses readers in character psyches without traditional breaks.^[79] In poetry, fluid meter—often blending iambic patterns with free verse—produces a natural cadence that evokes motion, as in Walt Whitman's Leaves of Grass, where long, enjambed lines foster a propulsive rhythm akin to breathing or wandering.^[80] Spoken word poetry extends flow into performance, where oral delivery relies on prosody—encompassing intonation, tempo, and pauses—to convey layered meanings and build intensity. Artists like Sarah Kay employ rhythmic phrasing to weave personal anecdotes into universal themes, using breath control and accentuation to maintain auditory momentum during live recitations.^[81] Culturally, flow's impact spans these domains through prosody metrics, such as syllable duration and stress alignment, which analysts use to quantify rhythmic efficacy in both musical tracks and literary readings, revealing how balanced prosody enhances coherence and affective resonance.^[82] The psychological flow state, involving deep immersion, has occasionally informed these artistic pursuits by encouraging creators to sustain uninterrupted creative rhythms.^[83]

Other Uses

Brands and Products

Flow Hive is a beehive system invented by Australian beekeepers Cedar and Stuart Anderson, along with engineer John Edom, and launched in 2015 through a successful Kickstarter crowdfunding campaign that raised over $13 million.^[84] The product features proprietary plastic frames with a breakable mid-wall that allows honey to flow directly into a collection tube when a key is turned, enabling extraction without opening the hive or disturbing the bees, thus reducing stress on the colony and the risk of stings for the beekeeper.^[85] As of early 2023, Flow Hive had sold more than 100,000 units worldwide, expanding to include models like the Flow Hive 2 and hybrid versions compatible with traditional Langstroth hives, promoting sustainable beekeeping practices.^[86]^[87] Flow is a task and project management software developed by the Canadian company GetFlow Inc., founded in 2013 and headquartered in Toronto.^[88] Designed for teams, it integrates features for organizing tasks, timelines, conversations, and file sharing in a unified interface, emphasizing simplicity and collaboration without the complexity of enterprise tools.^[89] The platform gained traction in the 2010s and 2020s for small to medium-sized teams, with mobile and desktop apps supporting real-time updates and automation of workflows, though it ceased operations on October 10, 2025, after serving users focused on productivity enhancement.^[90] Historically, Flow-Matic was an early programming language developed by Grace Hopper and her team at Remington Rand for the UNIVAC I computer between 1955 and 1959.^[91] Originally known as B-0 (Business Language version 0), it was the first to use English-like commands for data processing, influencing the design of COBOL by prioritizing readability for business applications over machine code.^[46] Though discontinued after its short operational period, Flow-Matic represented a pivotal product in the evolution of high-level languages, marking Remington Rand's contribution to accessible computing tools.^[92]

Sports and Recreation

In sports and recreation, the concept of flow manifests through dynamic physical practices that emphasize seamless movement, synchronization, and immersion, often enhancing participant engagement and skill development. Vinyasa flow yoga exemplifies this approach, involving a dynamic sequencing of poses synchronized with breath to create a continuous, fluid practice. Popularized by T. Krishnamacharya in the 1930s during his tenure at the Mysore Palace yogashala, where he developed Ashtanga Vinyasa Yoga tailored for active practitioners, this style integrates breath control (pranayama) with postural transitions to promote physical vitality.^[93] Practitioners experience benefits such as improved flexibility through sustained stretching and enhanced mindfulness via focused breathing, which fosters present-moment awareness during sequences.^[94]^[95] Flow arts represent another recreational domain where continuous motion is central, blending elements of dance, juggling, and object manipulation for expressive, rhythmic performances. Activities like juggling and poi spinning—tethered weights swung in geometric patterns—prioritize unbroken flow to achieve aesthetic harmony and personal satisfaction. The modern flow arts community emerged in the early 2000s, coalescing around rave culture, online forums, and festivals such as the 2005 Play Festival, where enthusiasts adopted the term "flow arts" to unify disciplines like poi (originating from Maori traditions but adapted for contemporary spinning) and club juggling.^[96] This post-2000s evolution has fostered global communities focused on skill-building through repetitive, meditative motion, often performed with LED or fire props for visual appeal.^[97] In broader sports contexts, flow riding simulates surfing on stationary artificial waves generated by machines like the FlowRider, allowing riders to perform endless maneuvers on a thin sheet of recirculating water. Invented by Tom Lochtefeld, the first FlowRider debuted in 1991 at Schlitterbahn waterpark in Texas, stemming from his 1980s experiments to democratize wave access.^[98] Riders use flowboards or bodyboards to carve and spin, emphasizing balance and adaptive technique on the engineered wave surface. Similarly, in snowboarding, "flow" describes a smooth carving technique where riders link edge-to-edge turns with minimal skidding, leveraging the board's sidecut for precise, rhythmic descents that prioritize speed and control.^[99] This fluid style, often called "flowing carves," enhances run efficiency and stylistic expression on groomed slopes.^[100]

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In this article, we will explain the flow state of mind, flow activities, examples of flow in action, and how to achieve it.What Is a Flow State of Mind? · Examples of Flow in Action · Flow State Training...
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Applying Positive Psychology in Sport: A Trainee's Case Study
Jun 17, 2024 · The aim of this case study is to provide practitioners with insight into the impacts of a positive psychology intervention on confidence and performance.
[34]
(PDF) Mindfulness and Flow: Tools from Sports Psychology for ...
Aug 14, 2025 · Flow interventions complement these benefits by fostering deep task immersion and a sense of control, which are associated with resilience and ...<|separator|>
[35]
Neurocognitive mechanisms underlying the experience of flow
It is proposed that a necessary prerequisite to the experience of flow is a state of transient hypofrontality that enables the temporary suppression of the ...
[36]
Neurocognitive mechanisms underlying the experience of flow
It is proposed that a necessary prerequisite to the experience of flow is a state of transient hypofrontality that enables the temporary suppression of the ...
[37]
Cash Flow Statements: How to Prepare and Read One - Investopedia
A cash flow statement shows how money flows in and out of a company through operations, investments, and financing activities. The cash flow statement ...Accrual accounting · Working Capital · Capital expenditures (CapEx)
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6.7 Classification of cash flows - PwC Viewpoint
If a cash flow does not meet the definition of an investing activity or a financing activity, the cash flow is classified as an operating activity. Cash flows ...
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Free Cash Flow (FCF): How to Calculate and Interpret It - Investopedia
FCF can be calculated by starting with cash flows from operating activities on the statement of cash flows, because this number will have already adjusted ...What Is Free Cash Flow? · Understanding FCF · Calculating FCF · Limitations
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Information Distortion in a Supply Chain: The Bullwhip Effect
The effect of flexible lead times on a paper producer ... Padmanabhan, Seungjin Whang, (1997) Information Distortion in a Supply Chain: The Bullwhip Effect.
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Business Process Model & Notation™ (BPMN™)
The Business Process Model and Notation (BPMN) specification provides a graphical notation for specifying business processes in a Business Process Diagram.
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Value Stream Mapping Overview - Lean Enterprise Institute
Value-stream mapping (VSM) diagrams all steps from order to delivery, mapping current and future states to identify and eliminate waste.
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[PDF] Wassily Leontief and the discovery of the input-output approach
The paper is about Wassily Leontief's path towards the discovery of input-output economics, published in the Review of Economic Statistics in 1936 and 1937 ...
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Liquidity Risk and Credit in the Financial Crisis - San Francisco Fed
May 14, 2012 · The 2007–08 financial crisis was the biggest shock to the banking system since the 1930s, raising fundamental questions about liquidity risk.
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Grace Hopper Writes "Flow-Matic" for the UNIVAC II, the First ...
In 1957 Grace Hopper Offsite Link wrote the first English-like data-processing compiler, FLOW-MATIC Offsite Link for the UNIVAC II.
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Control flow - Glossary - MDN Web Docs
Jul 11, 2025 · Control flow is the order in which the computer executes statements in a script. Code is run in order from the first line in the file to the last line.
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ISO 5807:1985 - Information processing
In stockDefines symbols to be used in information processing documentation and gives guidance on conventions tor their use in data flowcharts, program flowcharts, ...
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Dataflow Programming - Devopedia
Nov 17, 2020 · Dataflow programming (DFP) is a programming paradigm where program execution is conceptualized as data flowing through a series of operations or ...
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[PDF] The Semantics of a Simple Language for Parallel Programming
In this paper, we describe a simple language for parallel programming. Its semantics is studied thoroughly. The de- sirable properties of this language and its ...
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[PDF] maximal flow through a network - lr ford, jr. and dr fulkerson
Introduction. The problem discussed in this paper was formulated by. T. Harris as follows: "Consider a rail network connecting two cities by ...
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Apache Airflow
Apache Airflow is a platform to programmatically author, schedule, and monitor workflows using Python, and is easy to use for anyone with Python knowledge.Workflows as code · Use Cases · Tutorials · Installation of Airflow
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RxJS
RxJS is a library for reactive programming using Observables, to make it easier to compose asynchronous or callback-based code.Overview · API List · Operators · Observable
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Process flow diagram - processdesign
Mar 2, 2015 · The process flow diagram is an essential part of chemical engineering. It conveys a process and the path of its individual components.Overview · Process Topology · Stream Information · Equipment Information
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Continuity Equation - Fluid Flow - Engineering Library
One of the simplest applications of the continuity equation is determining the change in fluid velocity due to an expansion or contraction in the diameter of a ...
[55]
[PDF] Optimization of Material Flow by Lean Tools and RFID Integration ...
This thesis outlines a systematic problem-solving approach, starting with process visualization through Value. Stream Mapping (VSM), problem identification by ...
[56]
RFID and Supply Chain Management for Manufacturing Digital ...
The system should enhance the visibility of information and material flows in the internal as well as external supply chain, thus a more effective and ...3.1. Rfid And Supply Chain... · 4. Overview Of Rfid... · 4.1. Rfid System
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Enhancing supply chain performance using RFID technology and ...
This study carries out a systematic literature review of research articles published during the timeline (2000-2021) that discuss the role of RFID technology ...2.1. Rfid Technology And... · 3. Rfid Applications · 3.2. Rfid In Smart...Missing: JIT | Show results with:JIT
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Fluid Flow - Equation of Continuity - The Engineering ToolBox
This statement is called the Equation of Continuity. Common application where the Equation of Continuity are used are pipes, tubes and ducts with flowing fluids ...
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Assembly Line Revolution | Articles - Ford Motor Company
Sep 3, 2020 · Discover the 1913 breakthrough: Ford's assembly line reduces costs, increases wages and puts cars in reach of the masses.
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The upcoming 3D-printing revolution in microfluidics - PMC - NIH
3D-printing has recently attracted attention as a way to fabricate microfluidic systems due to its automated, assembly-free 3D fabrication, rapidly decreasing ...
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Making Flow – Interview with director Gints Zilbalodis - Blender
Jan 22, 2025 · In this interview, Gints Zilbalodis, writer and director of the film, shares how Blender was instrumental in the creation of the film.
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Flow (2024) - IMDb
Rating 7.9/10 (99,036) "Flow," the latest work from Latvian director Gints Zilbalodis, is one of those rare films that transcends the need for dialogue and speaks directly to the soul ...Gints Zilbalodis · Flow · Flow Trailer · Flow, le chat qui n'avait plus...
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How do you survive the end of the world? Oscar-nominated 'Flow ...
Feb 24, 2025 · The movie follows a black cat and the small menagerie of animals it meets as they sail over a drowned landscape, encountering survivors amid abandoned cities.<|control11|><|separator|>
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Flow (2024) | Rotten Tomatoes
Rating 97% (193) From the boundless imagination of the award-winning Gints Zilbalodis (Away) comes a thrilling animated spectacle as well as a profound meditation on the ...Gints Zilbalodis · Flow: Trailer 1 · 193 Reviews · Audience Reviews
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Baltic Animation Still in Full 'Flow': 'Smallness Can Be a Superpower'
Jun 9, 2025 · Oscar-winning “Flow” by Latvia's Gints Zilbalodis brought Baltic animation to new heights. Now, local creators are figuring out how to benefit from the ...
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'Flow' becomes first Latvian film to win Academy Award for animated ...
“Flow,” a wordless cat parable, won the Oscar for animated feature at Sunday's 97th Academy Awards.
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Aqua (Short 2012) - IMDb
Rating 6.3/10 (173) Aqua: Directed by Gints Zilbalodis. The tale of a cat who is caught in a world of water and needs to adapt to survive.
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"Aqua" by Gints Zilbalodis - Cartoon Brew
Aqua is quite a sophisticated piece of visual storytelling for a 17 year-old. Created with Toon Boom Animate Pro, After Effects and Photoshop.
[69]
Aqua - Vimeo
Feb 7, 2012 · A cat wakes up surrounded by water and must learn to survive. Check out my other animated short films; Inaudible - vimeo.com/131109262 ...
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The Secret Life of Waves - BBC Four
The Secret Life of Waves ... David Malone's documentary delves into the secrets of ocean waves, revealing that waves are not made of water, that some waves travel ...
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The Secret Life of Waves (TV Movie 2011) - IMDb
Rating 6.6/10 (26) The Secret Life of Waves ... David Malone delves into the secrets of ocean waves. In an elegant and original film, he finds that waves are not made of water, that ...
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2012 - Flow State | Warren Miller Entertainment
In 2012, Warren Miller Entertainment introduced its 63rd film, Flow State. · The 2012 session guides you to the top of the world's most striking peaks in Japan, ...Missing: documentary | Show results with:documentary
[73]
On the Metrical Techniques of Flow in Rap Music
[6] As used in this article, “flow” describes all of the rhythmical and articulative features of a rapper's delivery of the lyrics. Though rappers rarely ...
[74]
Vocal Pitch in Rap Flow – Intégral - Music Theory
The regularity of Eminem's pitched rhythmic layer contrasts his usually irregular and complex rhyme schemes, and is underscored by an atypically straightforward ...
[75]
Jazz Improvisation: The Ultimate Guide to Learn - Jazzadvice
In learning how to improvise, there's this constant flow of learning new material, learning old material better or completely reworking it, discovering new ...
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Go with the Flow - Song by Queens of the Stone Age - Apple Music
Listen to Go with the Flow by Queens of the Stone Age on Apple Music. 2002. Duration: 3:07.
[77]
(PDF) What Is Musical Prosody? - ResearchGate
Aug 10, 2025 · Musical prosody is a complex, rule-governed form of auditory stimulation, and it can move listeners emotionally in systematic ways.
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[PDF] A Stylistic Analysis of Stream-of-Consciousnes Narration in James ...
Abstract. The researchers studied James Joyce's revolutionary stream-of-consciousness narration techniques in Ulysses as found in Chapter Nine: The Cyclops.
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Poetry 101: What Is Meter? Learn the Difference Between ...
Aug 5, 2021 · Examples of Meter in Poetry A good example of this is “iambic pentameter,” which can be found in English language poetry across many centuries. ...
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Flow | The Poetry Foundation
Oct 18, 2023 · Flow exists where the surplus of energy bubbles at the surface of what is intelligible. It is the river that carries meaning but does not need meaning to carry ...
[81]
Prosody in Music and Songwriting - Berklee Online Take Note
May 28, 2022 · The definition of prosody is when all elements work together to support the central message of the song, an appropriate relationship between the elements.
[82]
Brain Scans of Jazz Musicians Reveal How to Reach a Creative ...
May 30, 2024 · Our study examined flow in the context of jazz improvisation. Jazz has been used in several previous studies of creative production because ...
[83]
An Ingenious Invention That Turns Beehives Into Flowing Honey Taps
Feb 25, 2015 · In a nutshell, Flow frames have a partially formed honeycomb matrix within a transparent frame. Bees complete the comb, fill the cells with ...
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https://www.wired.com/2015/02/flow-hive/
[85]
A Beehive That Takes the Sting Out of the Harvest
May 30, 2015 · In a backyard shed, he and his father, Stuart, invented an alternative setup called Flow Hive, and this year they began to sell it. Domesticated ...
[86]
Flow - Crunchbase Company Profile & Funding
Flow is an all-in-one tool that helps your team achieve more. It handles tasks, projects, timelines, messaging, and team communication.
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Flow - Project and Task Management Software for Teams
Flow is project management software that simplifies teamwork. Use it to plan projects, prioritize to-dos, delegate tasks, and collaborate beautifully.
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Project management workflow: all you need to know - GetFlow
Dec 23, 2022 · GetFlow will shut down on October 10, 2025. ... If you are already working with a project management tool like Flow, it's likely that it will ...
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FLOW-MATIC Programming Language Information & Resources
It was developed for the UNIVAC I at Remington Rand under Grace Hopper from 1955 to 1959, and helped shape the development of COBOL. Wikipedia. Created Year: ...
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[PDF] Early programming languages - Stanford University
• FLOW-MATIC (1955) … which begat COBOL… • FORTRAN (1956). (the oldest ... Remington Rand refused to give her a team to work on programming language ...<|control11|><|separator|>
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Krishnamacharya's Legacy: Modern Yoga's Inventor | History of Yoga
Jan 20, 2025 · Thus began one of Krishnamacharya's most fertile periods, during which he developed what is now known as Ashtanga Vinyasa Yoga.Emerging From The Shadows · Developing Ashtanga Vinyasa · Instructing IyengarMissing: flow | Show results with:flow
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What Are the Top Health Benefits of Yoga? - CU Anschutz newsroom
Jun 14, 2023 · Mobility and flexibility. The benefits that immediately come to mind are mobility and flexibility. · Balance · Mindfulness · A body connection.
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10 Benefits of Yoga & Why You Should Give It a Try | USU
Jul 5, 2024 · It's known to improve flexibility, build strength, reduce stress, and enhance mindfulness. Vinyasa: Vinyasa is a slighter faster pace than hatha ...
[94]
The History of the Term "Flow Arts"
First, people began spinning and rolling objects at raves in hotspots around the world. In 2001 the legendary Drone was a spot in London where jugglers went to ...
[95]
What is Flow Arts?
Flow Arts is a general term used to describe the intersection of a variety of movement-based disciplines including dance, juggling, fire-spinning, and object ...Missing: continuous | Show results with:continuous
[96]
The History of Stationary Wave Machines - FlowRider
May 10, 2022 · FlowRider was inspired in the 1980s, the first wave debuted in 1991, and the first FlowTours were in the late 1999s/early 2000s. FlowRider has ...Missing: 1997 artificial
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Tag Archives: Snowboard Carving - Flowing Freeride
Mar 9, 2018 · Carving is riding and balancing on the snowboard edge and sidecut. Your back foot follows your front foots direct path and you're not skidding.
[98]
Advance Snowboard Carving Surfer Turns & Grab Carves
Sep 20, 2018 · Carving is when you're using your sidecut and eliminate the pivot/rotation movement in your snowboard and body. You're balanced on your edge ...
[99]
How free solo climber Alex Honnold conquered El Capitan - Red Bull
Feb 8, 2019 · As shown in the film Free Solo, Honnold made an attempt to climb Freerider in 2017 but backed off around 275m [900ft] up on the Freeblast slabs, ...
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The Strange Brain of the World's Greatest Solo Climber - Nautilus
Aug 3, 2016 · When I ask Honnold to describe the ideal free-solo psychological experience, he says, “You get into positions where you're like, this is so ...