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RSA

The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key encryption algorithm invented in 1977 by Ronald Rivest, Adi Shamir, and Leonard Adleman at MIT, enabling secure data transmission and digital signatures by exploiting the computational infeasibility of factoring the product of two large prime numbers into its components.^[1]^[2]^[3] The system generates a public key for encryption from the product of primes and a corresponding private key derived from those primes, allowing anyone to encrypt messages while only the private key holder can decrypt them, a breakthrough that eliminated the need for symmetric key exchange over insecure channels.^[4]^[5] RSA's foundational role in asymmetric cryptography underpins protocols like SSL/TLS for web security, secure email, and VPNs, with its inventors receiving the Turing Award in 2002 for advancing computational complexity theory and practical security systems.^[2]^[6] Despite enduring over four decades of cryptanalytic scrutiny—including side-channel attacks, chosen-ciphertext vulnerabilities when poorly implemented, and the 1994 factorization of RSA-129 after years of distributed effort—properly configured RSA with sufficient key lengths (e.g., 2048 bits or more) remains secure against classical computing threats, as no general efficient factoring algorithm has emerged.^[2]^[5] Emerging quantum computing capabilities, however, pose a long-term risk via algorithms like Shor's that could factor large semiprimes efficiently, prompting transitions to post-quantum alternatives while RSA continues in hybrid schemes.^[7]^[2]

Organizations

Academic and research institutions

The Royal Society for the Encouragement of Arts, Manufactures and Commerce (RSA), founded in 1754 by William Shipley in London, England, operates as a registered charity dedicated to advancing societal progress through practical initiatives in the arts, manufacturing, and commerce. It fosters innovation by supporting empirical projects, awarding fellowships to influential thinkers, and facilitating discourse on evidence-based solutions to public challenges, thereby contributing to intellectual and economic development since its inception.^[8] The Regional Studies Association (RSA), an international learned society, examines regional economic, social, and spatial dynamics through interdisciplinary analysis grounded in empirical evidence from academics, policymakers, and practitioners.^[9] Established with the launch of its flagship journal Regional Studies in 1967 under editor Peter Hall, it emphasizes systematic connections across disciplines to understand regional contingencies in economic and political processes.^[10] Its activities include knowledge exchange via conferences and publications, promoting data-informed insights into urban and regional planning without prescriptive policy advocacy.^[11] The Research Society on Alcoholism (RSA), formed in 1976, serves as a professional forum for scientists investigating the biological, physiological, cognitive, and social dimensions of alcohol use disorders and related effects.^[12] It supports career development for researchers, particularly emerging scholars, by hosting annual scientific meetings that disseminate findings from controlled studies and clinical data, while emphasizing rigorous, multidisciplinary approaches to alcohol-related problems.^[13] The society's efforts prioritize advancing foundational knowledge over applied interventions, drawing on peer-reviewed contributions to inform broader biomedical understanding.^[14]

Military and defense

The Royal New Zealand Returned and Services' Association (RSA) operates as a nationwide network supporting welfare needs of military veterans, current service personnel, and their families through advocacy and practical assistance.^[15] Established as one of New Zealand's largest voluntary organizations, it facilitates access to government resources including Veterans' Affairs benefits, accident compensation via ACC, and income support, drawing on a support structure covering the entire country.^[16] Funding derives primarily from member subscriptions, donations, and collaborative grants from entities like Veterans' Affairs, which allocated resources to the RSA for veteran programs as of July 2025.^[17] In July 2025, the RSA initiated a strategic relaunch emphasizing direct veteran aid over legacy club functions, targeting younger post-operational personnel amid recognition that traditional models inadequately addressed modern service-related challenges such as mental health and reintegration.^[18] ^[19] This evolution aligns with defense imperatives for sustained personnel readiness by bolstering post-service stability, informed by feedback from retired senior officers highlighting gaps in support for contemporary conflicts and peacekeeping missions.^[19] A Runway Safety Area (RSA) constitutes a cleared, obstacle-free zone adjacent to runways, engineered to accommodate aircraft deviations like overruns, undershoots, or veer-offs, thereby minimizing injury and damage risks in high-stakes operations.^[20] U.S. Air Force doctrine mandates RSAs for military airfields, defining them as areas surrounding the runway usable in emergencies, with dimensions calibrated from runway excursion incident data showing these events as a primary aviation hazard.^[21] Standard RSA specifications for operations involving larger military aircraft prescribe a 500-foot width centered on the runway and 1,000-foot extensions beyond each end, a configuration substantiated by empirical reviews of excursion kinematics and historical accident severities to optimize deceleration and containment.^[22] In defense contexts, such as tactical fighter bases, RSAs enhance sortie generation rates by reducing downtime from mishaps, with compliance enforced through engineering assessments prioritizing graded, low-friction surfaces over engineered materials where terrain constraints apply.^[21]

Commercial and other organizations

RSA Security LLC is a cybersecurity firm focused on identity and access management solutions, including risk-based authentication and fraud prevention tools. Founded in 1982 by Ronald Rivest, Adi Shamir, and Leonard Adleman—the developers of the RSA encryption algorithm—it commercialized public-key cryptography for enterprise use, enabling secure data transmission and digital signatures in commercial applications. The company gained prominence through products like SecurID tokens, which provide hardware-based two-factor authentication via time-synchronized codes, adopted widely for protecting network access in businesses.^[23]^[24] RSA Security expanded through innovations in public-key infrastructure (PKI) services, offering certificates and keys for e-commerce and secure communications, with empirical testing via its Cryptolaw or Die! column in industry publications to validate security claims against real-world threats. In 2006, it was acquired by EMC Corporation for $2.1 billion, integrating its technologies into enterprise storage and security portfolios. After EMC's merger with Dell in 2016, RSA continued as a division until Dell divested it to private equity firm STG Partners in February 2020 for $2.075 billion, allowing focused investment in cloud-native identity solutions amid rising cyber risks.^[25]^[26] The Rehabilitation Services Administration (RSA), a division of the U.S. Department of Education's Office of Special Education and Rehabilitative Services, administers federal grants for vocational rehabilitation programs targeting individuals with disabilities. Established under the Rehabilitation Act of 1973, RSA allocates formula grants to state agencies to deliver services such as vocational evaluation, training, assistive technology, and job placement, with program efficacy tracked via metrics like competitive employment rates and earnings data reported annually. In fiscal year 2023, RSA oversaw programs serving over 1 million individuals, emphasizing evidence-based outcomes to promote self-sufficiency through measurable workforce integration.^[27]^[28]^[29]

Geographical places

Sovereign states and regions

The Republic of South Africa (RSA) is a sovereign state at the southern tip of the African continent, with its formal name adopted on May 31, 1961, upon becoming a republic independent from the British monarchy. The abbreviation RSA derives directly from "Republic of South Africa" and is used officially in contexts such as international sports by the International Olympic Committee.^[30] Following the end of apartheid, the first multiracial democratic elections on April 27, 1994, marked a transition to inclusive governance, culminating in the adoption of a new constitution on December 18, 1996, which established a unitary parliamentary republic with a president serving as both head of state and government.^[31] This framework divides powers among executive, legislative, and judicial branches, with the National Assembly and National Council of Provinces forming a bicameral legislature representing the nation's nine provinces.^[32] As of mid-2025, RSA's population is estimated at 64.7 million, characterized by a youthful structure where children and youth under 35 comprise over 37% of residents, alongside a diverse ethnic composition dominated by Black Africans at approximately 80%, followed by Coloured (mixed-race), White, and Indian/Asian groups.^[33] Urbanization stands at over 68%, with major concentrations in Gauteng province, reflecting migration patterns driven by economic opportunities and historical legacies.^[33] Life expectancy has improved post-1994 due to expanded healthcare access, though challenges persist from HIV/AIDS prevalence and infrastructure strains.^[33] Economically, RSA operates as an upper-middle-income nation with a GDP of roughly $400 billion in nominal terms as of 2024, though annual growth has averaged under 1% over the past decade amid energy shortages, logistical bottlenecks, and fiscal constraints.^[34] Key sectors include mining (gold, platinum, diamonds), manufacturing, and services, with exports heavily reliant on commodities; unemployment hovers above 30%, exacerbating inequality where the Gini coefficient exceeds 0.63.^[34] Governance under the 1996 constitution emphasizes human rights and separation of powers, yet implementation faces criticism for state capture, policy uncertainty, and slow structural reforms, as evidenced by subdued growth projections of 1.3% for 2024 and 1.6% for 2025.^[35]^[36]

Localities and infrastructure

In aviation, a Runway Safety Area (RSA) is a standardized infrastructure feature at airports, consisting of a cleared, graded, and obstacle-free surface surrounding the runway ends to mitigate risks from aircraft overruns, undershoots, or veer-offs. The U.S. Federal Aviation Administration (FAA) specifies that RSAs for most runways under 4,500 feet (1,372 meters) in length should extend 500 feet (152 meters) wide, centered on the runway centerline, and 1,000 feet (305 meters) beyond each runway end, with the surface capable of supporting an aircraft's weight and reducing deceleration forces through materials like turf or stabilized soil.^[20] These areas enhance safety by providing a buffer zone that minimizes damage potential, as evidenced by FAA data showing RSAs contributing to reduced excursion severity in incidents.^[20] Engineered variants, such as Engineered Material Arresting Systems (EMAS), may supplement traditional RSAs at constrained sites, using crushable concrete blocks to absorb kinetic energy from overrunning aircraft, as implemented at over 80 U.S. airports since the early 2000s.^[20] Internationally, similar standards apply under ICAO Annex 14 guidelines, recommending RSA dimensions based on aircraft category and runway use, though compliance varies by nation. In U.S. telecommunications, Rural Service Areas (RSAs) denote 428 designated geographic zones established by the Federal Communications Commission (FCC) in 1995 for auctioning cellular licenses in non-metropolitan regions, covering approximately 90% of U.S. land area but only 6% of the population to promote infrastructure deployment in underserved locales. These polygonal boundaries, derived from census and economic data, exclude urban Metropolitan Service Areas (MSAs) and enable targeted broadband and mobile network expansion, with ongoing FCC spectrum reallocations supporting 5G infrastructure as of 2023.

Technology and computing

Cryptography and cybersecurity

The RSA cryptosystem, an asymmetric encryption algorithm, was proposed in 1977 by Ronald Rivest, Adi Shamir, and Leonard Adleman at the Massachusetts Institute of Technology.^[5] It operates on the computational difficulty of factoring the product of two large prime numbers, enabling secure public-key encryption and digital signatures without prior shared secrets.^[37] The system generates a public key from a modulus N = p × q (where p and q are large primes) and other parameters, while the private key derives from the factors p and q; encryption uses the public exponent e, and decryption leverages the private exponent d.^[5] Rivest, Shamir, and Adleman received a U.S. patent for the algorithm on September 20, 1983, which expired on September 21, 2000, after which unrestricted commercial use became possible.^[38] RSA's security rests on the empirical observation that no classical algorithm has practically factored large semiprimes used in production keys, despite intensive efforts; for instance, the RSA Factoring Challenge (initiated in 1991) saw its largest solved instance, RSA-250 (a 250-decimal-digit or 829-bit number), factored in December 2020 by a distributed computing consortium using the general number field sieve.^[39] This resistance has validated RSA's integration into protocols like TLS and SSL for key exchange and certificate authentication, where it secures billions of daily web transactions by ensuring server identity and initial session key protection.^[40] However, TLS 1.3 (standardized in 2018) deprecated RSA for key exchange in favor of ephemeral Diffie-Hellman variants to mitigate certain risks, though RSA remains common for signatures.^[41] Quantum computing poses a fundamental threat to RSA via Shor's algorithm, which efficiently factors large integers on a sufficiently powerful quantum device, potentially rendering 2048-bit keys insecure.^[42] A May 2025 preprint from Google Quantum AI researcher Craig Gidney estimates that RSA-2048 could be factored in under one week using fewer than one million noisy qubits, a reduction from prior estimates requiring billions of logical qubits, by optimizing quantum circuit depth and error correction overhead.^[43] This advances underscore causal vulnerabilities in RSA's factorization assumption under quantum conditions, prompting accelerated transitions; the National Institute of Standards and Technology (NIST) selected CRYSTALS-Kyber, a lattice-based key encapsulation mechanism, in July 2022 as a post-quantum alternative for general encryption, with standards finalized as FIPS 203 in August 2024.^[44] Critics note that over-reliance on RSA's unproven classical hardness has delayed hybrid and post-quantum migrations, risking "harvest now, decrypt later" attacks where encrypted data is stored for future quantum decryption.^[45]

Other computing and engineering applications

Response Spectrum Analysis (RSA) serves as a linear dynamic procedure in structural engineering for estimating peak structural responses—such as displacements, velocities, accelerations, and forces—during seismic events without performing full time-history simulations. By leveraging pre-defined response spectra derived from historical or design earthquake records, RSA applies these spectra to the structure's modal properties to compute modal contributions, which are then combined via methods like the square root of the sum of squares (SRSS) or complete quadratic combination (CQC) to yield approximate maximum values. This approach, rooted in statistical aggregation of modal responses, enables efficient evaluation of multi-degree-of-freedom systems under broadband excitation.^[46]^[47] In computing applications, RSA is integrated into finite element analysis (FEA) software packages, where algorithms process the structure's mass and stiffness matrices to extract natural modes and frequencies, subsequently scaling spectral ordinates to modal forces for static-like equilibrium checks. For instance, tools like ETABS or SAP2000 implement RSA by first conducting eigenmode extraction—typically retaining modes up to 90% of the structure's mass participation—before applying directional spectra (e.g., from ASCE 7-22 standards) along principal axes, often incorporating factors for modal orthogonality and damping ratios of 5% as standard. This computational efficiency contrasts with nonlinear time-history analysis, allowing engineers to iterate designs rapidly for compliance with seismic codes like Eurocode 8, which mandates RSA for irregular structures exceeding certain height thresholds.^[48]^[47] Engineering implementations extend RSA to specialized domains, including bridge design where it assesses pier forces under site-specific spectra, or dam analysis incorporating hydrodynamic effects via added mass approximations. A 2013 study on concrete gravity dams refined RSA by including dam-water-foundation interaction, demonstrating that uncoupled models overestimate base shear by up to 20% compared to coupled variants, validated against centrifuge tests. Limitations include its assumption of linearity and peak superposition, which may underpredict responses in highly nonlinear scenarios, prompting hybrid use with pushover methods in performance-based design. Overall, RSA's algorithmic simplicity facilitates its adoption in simulation workflows, prioritizing conservative envelope estimates for safety-critical infrastructure.^[49]^[50]

Natural sciences

Biology, chemistry, and medicine

In structural biology and biochemistry, relative solvent accessibility (RSA) quantifies the exposure of amino acid residues to solvent in a folded protein, expressed as the ratio of its accessible surface area to that in a reference unfolded tripeptide (typically 0-1 scale, using a 1.4 Å probe radius). This metric, derived from atomic coordinates in X-ray crystallography or NMR structures, elucidates hydrophobic core burial (low RSA for nonpolar residues) versus surface exposure (high RSA for charged/polar ones), correlating with functional sites, folding stability, and evolutionary constraints where buried residues show higher conservation. RSA predictions from sequence alone achieve ~0.07 Å² accuracy via machine learning on datasets like CASP, aiding drug design by identifying ligand-binding pockets.^[51]^[52]^[53] RsaI, a type II restriction endonuclease from Rhodopseudomonas sphaeroides, recognizes the palindromic sequence 5'-GT^AC-3' and generates blunt-ended fragments, with optimal cleavage at 37°C in buffers containing Mg²⁺. Isolated in 1978, it digests 1 μg of λ DNA in 1 hour per unit, enabling precise DNA fragmentation for recombinant DNA techniques, polymorphism detection via RFLP, and subcloning; isoschizomers include AfaI and CviQI, but RsaI's star activity is minimized under standard conditions.^[54]^[55] In ophthalmology research, rabbit serum albumin (RSA) serves as a carrier protein in immunoassays for detecting retinal pigment epithelium (RPE)-specific autoantibodies, relevant to immune responses in transplantation models for inherited retinal dystrophies. For instance, RPE65, a 65 kDa RPE enzyme catalyzing isomerohydrolase activity in the visual cycle to regenerate 11-cis-retinal, underlies ~2% of recessive retinitis pigmentosa and ~16% of Leber congenital amaurosis (LCA) cases when biallelic mutations disrupt retinoid recycling, causing photoreceptor atrophy by age 2-5 years. Voretigene neparvovec-rzyl (Luxturna), an AAV2/5 vector expressing RPE65 cDNA via subretinal delivery, was approved by the FDA on December 19, 2017, for patients ≥12 months with confirmed biallelic RPE65 variants and sufficient viable photoreceptors; phase III trials reported 2-line improvements in mobility navigation under low light (p<0.001).^[56]^[57]^[58] In cardiovascular medicine, respiratory sinus arrhythmia (RSA) describes phasic heart rate variations tied to respiration—accelerating ~10-20 bpm during inspiration via reduced vagal inhibition and decelerating during expiration—predominantly in youth, with amplitude quantified as peak-valley RR interval differences or high-frequency power (0.15-0.40 Hz) via ECG spectral analysis. RSA indexes parasympathetic tone, attenuating with age (e.g., halving by age 60), autonomic dysfunction in diabetes (reduced by 30-50%), or heart failure (HF; <20 ms vs. >50 ms in controls), serving as a prognostic marker where low RSA predicts cardiovascular events (HR 1.5-2.0).^[59]^[60] Radiostereometric analysis (RSA), developed in the 1970s, uses implanted 0.8-1.0 mm tantalum beads (6-10 per bone/prosthesis) and simultaneous biplanar radiographs calibrated by a cage to measure 3D translations/rotations with 0.05-0.1 mm precision, tracking early postoperative migration in joint arthroplasties. In total hip replacements, subsidence >0.2 mm or rotation >1° within 2 years forecasts 85-90% aseptic loosening risk at 10 years; similarly for knees, where tibial component migration >0.5 mm correlates with revision (p<0.01).^[61]^[62]

Physics, mathematics, and other sciences

In mathematics, Random Structures and Algorithms (RSA) is a peer-reviewed journal dedicated to theoretical and empirical research in probabilistic combinatorics, random graphs, and related algorithmic problems. Established in 1990 by Ronald Graham, it was the first dedicated outlet for work in probabilistic combinatorics, emphasizing rigorous proofs and asymptotic analysis of random discrete structures.^[63] The journal, published by Wiley, covers topics such as the emergence of giant components in random graphs and factors in random bipartite matching, with an h-index of 73 as of recent assessments.^[64] In statistical physics and applied mathematics, random sequential adsorption (RSA) models irreversible deposition processes where particles or objects are sequentially placed at random positions on a substrate, adhering only if they do not overlap existing ones, leading to jamming at finite coverage. This nonequilibrium model, solvable exactly in one dimension for monodisperse segments yielding a saturation density of $1 - e^{-2} \approx 0.8649, extends to higher dimensions via simulations for hard spheres or disks, revealing packing fractions around 0.547 for 2D disks.^[65]^[66] RSA applies to packing problems, such as polydisperse ellipsoids or rounded polygons, where Monte Carlo methods validate densities against equilibrium limits, highlighting void formation and percolation thresholds absent in reversible adsorption.^[67]^[68] In statistical mechanics, RSA simulates surface adsorption and colloidal jamming, with extensions incorporating defects or self-avoiding chains to predict phase transitions, corroborated by experimental analogies in thin-film deposition.^[69]^[70]

Other uses

[Other uses - no content]

References

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An encryption method is presented with the novel property that publicly re- vealing an encryption key does not thereby reveal the corresponding decryption key.
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Definitions: Algorithm developed by Rivest, Shamir and Adelman (allowed in FIPS 186-3 and specified in ANS X9. 31 and PKCS #1).
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The RSA cryptosystem is a public-key cryptosystem, widely used for secure communication and e-commerce applications. It is often used to encrypt messages ...Missing: Adleman | Show results with:Adleman
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The basic premise behind the RSA cryptosystem is that although multiplying two numbers is a simple process, factoring the product back into the original two ...
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Ronald Rivest, Adi Shamir, and Leonard Adleman developed the RSA system in 1977 [RSA78]; RSA stands for the first letter in each of its inventors' last names.
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The Regional Studies Association is a learned society concerned with the analysis of regions and regional issues. Through our international membership we ...Events & Webinars · 2025 RSA Annual Conference · Funding & Awards · About us
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Association information. The Regional Studies Association (RSA) is a learned society concerned with urban and regional planning and development. It focuses on ...
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Apr 5, 2019 · 3.2. Runway Safety Area (RSA). The RSA is an area surrounding the runway intended for use by aircraft in emergency situations; it is measured ...
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Learn about RSA, RSA Programs, Find RSA Programs, What's New, Discover What's New at RSA, Success Stories, View Recent Success Stories, Policy ReviewRSA Programs · RSA Mission · What's New in RSA · State VR Agencies
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A TLS handshake enables clients and servers to establish a secure connection and create session keys. Learn more about how a TLS vs SSL handshake works.
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Jan 13, 2023 · A Response Spectrum Analysis (RSA) is a linear (strains directly related to stresses) dynamic procedure that uses a structure's natural vibrations properties.
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Sep 26, 2024 · Response-spectrum analysis (RSA) is a linear-dynamic statistical analysis method which measures the contribution from each natural mode of vibration.
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Response Spectrum Analysis
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[49]
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Nov 2, 2017 · Detection of Retinal Pigment Epithelium-Specific Antibody in iPSC-Derived Retinal Pigment Epithelium Transplantation Models ... (RSA) in the serum.
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RPE65 gene: MedlinePlus Genetics
Oct 6, 2022 · The RPE65 gene provides instructions for making a protein that is essential for normal vision. The RPE65 protein is produced in a thin layer of cells at the ...Missing: RSA | Show results with:RSA
[58]
Mutations in the RPE65 gene in patients with autosomal recessive ...
Based on our results, mutations in the RPE65 gene appear to account for ≈2% of cases of recessive RP and ≈16% of cases of LCA.Missing: RSA | Show results with:RSA
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Sinus Arrhythmia - StatPearls - NCBI Bookshelf - NIH
Respiratory sinus arrhythmia is a common finding. It is a normal alteration in cardiac rhythm generated from the vagus nerve stimulation and changes in ...
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Respiratory Sinus Arrhythmia | Circulation
Heartbeat intervals in resting humans and animals show fluctuations linked with respiration, a phenomenon known as respiratory sinus arrhythmia (RSA). Since ...
[61]
Radiostereometric Analysis: The Hip - PMC - NIH
Radiostereometric analysis is an accurate method of determining the migration and wear of orthopaedic implants such as total hip arthroplasties.
[62]
The accuracy and precision of radiostereometric analysis in upper ...
Radiostereometric analysis (RSA) is an accurate method for measurement of early migration of implants. Since a relation has been shown between early ...
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Aug 16, 2020 · ... Random Structures and Algorithms as the very first research journal in probabilistic combinatorics. Let me place it in a historical perspective.
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Random Structures and Algorithms - SCImago
Random Structures and Algorithms ; Publisher. John Wiley and Sons Ltd ; SJR 2024. 1.055 Q1 ; H-Index. 73 ; Publication type. Journals ; ISSN. 10429832, 10982418 ...
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[PDF] Multidisperse Random Sequential Adsorption and Generalizations
In this paper, we present a unified study of the limiting density in one-dimensional random sequential adsorption (RSA) processes where segment lengths are.
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Exactly solvable disordered sphere-packing model in arbitrary ...
Mar 9, 2006 · We introduce a generalization of the well-known random sequential addition (RSA) process for hard spheres in 𝑑 -dimensional Euclidean space ...
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[PDF] Random distribution of polydisperse ellipsoidal inclusions and ...
Sep 17, 2018 · This work proposes an extension of the well-known random sequential adsorption (RSA) method in the context of non-overlapping random mono- ...
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[PDF] Examination of saturation coverage of polygons using random ...
The random sequential addition (RSA) packing approach is a time-dependent process that is perhaps one of the most well-known nonequilibrium packing models. The ...
[69]
Random sequential adsorption with correlated defects
Jun 26, 2024 · The random sequential adsorption (RSA) problem holds crucial theoretical and practical significance, serving as a pivotal framework for ...
[70]
Random sequential adsorption of self-avoiding chains on two ...
Random sequential adsorption of extended objects deposited on two-dimensional regular lattices is studied. The depositing objects are chains formed by ...