CW
![Wave speed \mathbf{c}_{\mathrm{w}}][float-right]Continuous wave (CW) denotes an electromagnetic signal or waveform of unchanging amplitude and frequency, usually a pure sine wave, in contrast to modulated, pulsed, or damped variants.[1][2] This form enables efficient transmission by concentrating energy in a narrow bandwidth, making it foundational for applications requiring high signal-to-noise ratios.[3] CW operation emerged in the early 20th century with the advent of vacuum tube oscillators, supplanting inefficient spark-gap transmitters that produced broadband damped waves, and it remains prevalent in amateur radio for Morse code telegraphy due to its simplicity and range effectiveness.[4] In optics and lasers, CW mode signifies steady output without pulsing, supporting precise spectroscopy and machining, while in radar, unmodulated CW leverages the Doppler effect for velocity measurement, though it lacks range resolution without frequency modulation.[1] Defining characteristics include minimal spectral occupancy and robustness against interference, with no notable controversies beyond historical transitions from older technologies.[5]
Science and engineering
Continuous wave
A continuous wave (CW) is an electromagnetic wave characterized by constant amplitude and frequency, typically represented as a sinusoidal oscillation that persists indefinitely without interruption or pulsing.[2][1] This contrasts with pulsed waves, where energy is emitted in discrete bursts, allowing CW sources to deliver steady power output suitable for sustained operations.[6] In mathematical analysis, CW signals are idealized as infinite-duration sine waves, facilitating modeling in fields like signal processing and wave propagation.[7] In radio transmission, CW originated as an early modulation technique where a carrier sine wave is intermittently switched on and off to encode information, such as Morse code, replacing less efficient spark-gap methods by the early 20th century.[8] Reginald Fessenden demonstrated practical CW transmission in 1906 from his Brant Rock station in Massachusetts, marking a pivotal advancement in radiotelegraphy by enabling clearer, longer-range signals with reduced bandwidth compared to amplitude-modulated alternatives.[9] Today, CW remains prevalent in amateur radio for its simplicity, low power requirements, and resilience in noisy environments, often operating below 1500 Hz bandwidth in HF bands.[10] CW operation extends to optical systems, particularly lasers, where continuous-wave lasers maintain steady output power without temporal fluctuations, distinguishing them from pulsed variants that deliver high peak intensities intermittently.[11] The first continuous-wave gas laser, a helium-neon (HeNe) model emitting at 632.8 nm, was achieved in 1961, enabling applications in alignment, interferometry, and holography due to its stable coherence.[12] Semiconductor CW lasers emerged commercially in 1975, operating at room temperature and wavelengths around 900 nm, revolutionizing compact devices for telecommunications and sensing.[13] In materials processing, CW lasers excel in welding and cutting thick metals, as their consistent energy input minimizes thermal distortion; for instance, CO2 CW lasers at 10.6 μm wavelength achieve cutting speeds up to 10 m/min on steel plates exceeding 20 mm thickness.[14] Beyond radio and optics, CW principles underpin radar systems, where unmodulated or frequency-modulated CW radars transmit continuous signals to measure velocity via Doppler shifts, achieving resolutions down to 0.1 m/s without range ambiguity in short-range applications like automotive collision avoidance.[2] In spectroscopy, CW sources facilitate near-infrared analysis in diffuse media, such as functional near-infrared spectroscopy (fNIRS), by injecting constant-intensity light and detecting attenuation for oxygenation mapping, with typical source-detector separations of 3-4 cm yielding penetration depths of 2-3 cm in tissue.[15] These implementations highlight CW's utility in scenarios prioritizing stability over peak power, though limitations include potential overheating in high-power optical uses and susceptibility to interference in unmodulated radio forms.[16]CW complex
A CW complex is a topological space constructed by inductively attaching cells of increasing dimension, providing a framework for studying homotopy types in algebraic topology. Formally, it consists of a space X partitioned into disjoint open cells e^\alpha of dimension n \geq 0, where the 0-cells are points, and higher-dimensional cells are attached via continuous maps \phi_\alpha: S^{n-1} \to X^{n-1} from the boundary sphere to the (n-1)-skeleton X^{n-1}, with the n-skeleton X^n formed as the quotient space obtained by identifying the boundaries accordingly. The topology on X is the weak topology, meaning a subset is open if its preimage under every characteristic map \Phi_\alpha: D^n \to X (extending \phi_\alpha) is open in D^n, and the complex satisfies closure-finiteness: the closure \overline{e^\alpha} intersects only finitely many other cells.[17] This structure was introduced by J. H. C. Whitehead in his 1949 papers on combinatorial homotopy, where "CW" denotes "closure-finite" and "weak topology," distinguishing it from simplicial complexes by allowing more flexible cell attachments while preserving essential homotopical properties. Whitehead's approach aimed to model homotopy equivalences through cellular mappings, enabling the development of combinatorial methods for classifying spaces up to homotopy. Unlike simplicial complexes, which require linear simplices, CW complexes permit arbitrary continuous attachments, making them suitable for approximating general topological spaces. Construction proceeds skeleton by skeleton: X^0 is a discrete set of 0-cells (points); for each n \geq 1, the n-cells are attached to X^{n-1} via maps from S^{n-1} that land in finitely many (n-1)-cells, ensuring the attaching map is cellular. The full space X = \bigcup_n X^n inherits the weak topology, which coincides with the quotient topology from the cell attachments and ensures compactness of skeleta under finite-type conditions. Subcomplexes are unions of cells closed under the attachment relations. Examples include spheres S^n (as a single 0-cell with an n-cell attached via constant map on S^{n-1}), projective spaces, and Moore spaces M(\mathbb{Z}/m, n), constructed by attaching an (n+1)-cell to S^n with degree-m map.[18] Key properties include the fact that CW complexes are locally contractible, have countable dense subsets if locally finite, and support cellular homology, where chain groups are free abelian on n-cells and boundaries arise from degrees of attaching maps. Every topological space admits a weak homotopy equivalent CW model (CW approximation theorem), and weak homotopy equivalences between CW complexes are homotopy equivalences (Whitehead theorem). Products of CW complexes may not be CW unless one is finite-dimensional or locally finite, as shown by Dowker's counterexample of infinite products embedding non-CW spaces. These features make CW complexes indispensable for computations in homotopy and homology, though they exclude pathological spaces like the long line.[18][19][20]Military and defense
Chemical warfare
Chemical warfare entails the intentional use of toxic chemicals or their precursors to cause death, injury, or incapacitation in military contexts, typically delivered via munitions, devices, or dispersal systems designed for such purposes.[21] These agents exploit the physiological vulnerabilities of the human body, often leading to rapid onset of symptoms ranging from respiratory failure to neurological shutdown, with effects persisting due to environmental contamination.[21] Unlike conventional explosives, chemical weapons prioritize area denial and psychological terror, as their invisible or delayed impacts amplify fear among troops and civilians.[22] The modern era of chemical warfare commenced during World War I, with Germany initiating large-scale deployment on April 22, 1915, at the Second Battle of Ypres, where approximately 5,730 cylinders released 168 tons of chlorine gas over a 6-kilometer front, breaching Allied lines and causing thousands of casualties through asphyxiation and panic-induced retreat.[23] Subsequent innovations included phosgene for its deadlier lung-irritating properties and mustard gas for blistering skin and mucous membranes, resulting in over 1.3 million total casualties across all belligerents, though fatalities comprised less than 1% of overall war deaths due to evolving protective measures like gas masks.[22] World War II saw restrained offensive use among major powers despite massive stockpiles—exceeding 100,000 tons by some estimates—owing to mutual deterrence and fears of retaliation, though Japan employed them against Chinese forces in limited instances.[24] Post-1945 conflicts highlighted persistent violations, with Iraq employing mustard gas, tabun, and sarin against Iranian troops starting in 1983 during the Iran-Iraq War, inflicting tens of thousands of casualties and later targeting Kurdish civilians in the 1988 Halabja attack, which killed around 5,000.[25] In Syria's civil war, the Assad government deployed sarin in a August 21, 2013, attack near Damascus, killing over 1,400, and chlorine in barrel bombs during the 2018 Douma incident, as verified by OPCW fact-finding missions despite regime denials.[26] Such uses underscore the challenges in enforcement, as non-state actors like ISIS also improvised chlorine and mustard attacks in Iraq and Syria from 2014 onward.[27] Chemical agents are categorized by mechanism of action:- Choking/pulmonary agents (e.g., chlorine, phosgene): Irritate and flood the lungs with fluid, causing drowning-like asphyxiation.[21]
- Blister/vesicant agents (e.g., sulfur mustard): Penetrate skin and tissues, inducing burns, blindness, and long-term cancers.[21]
- Blood agents (e.g., hydrogen cyanide): Bind to hemoglobin, blocking oxygen transport and leading to cellular hypoxia.[21]
- Nerve agents (e.g., sarin, VX): Inhibit acetylcholinesterase, triggering uncontrolled muscle contractions, respiratory arrest, and death within minutes.[21]