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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Generation of Fragment Angular Momentum in Fission

A recent analysis of experimental data [J. Wilson et al., Nature (London) 590, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only after scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model freya, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. We find that this counterexample invalidates the conclusion in [J. Wilson et al.] that uncorrelated spins must necessarily have been generated after scission (a potentious conclusion that would rule out all models that generate the fragment spins prior to scission). Furthermore, it was reported [J. Wilson et al.] that the mass dependence of the average fragment spin has a sawtooth structure. We demonstrate that such a behavior naturally emerges when shell and deformation effects are included in the moments of inertia of the fragments at scission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Algebraic Theory of Patterns as Generalized Symmetries

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Characterizing photovoltaic backsheet adhesion degradation using the wedge and single cantilever beam tests, Part II: Accelerated tests

Photovoltaic (PV) backsheets provide critical moisture, mechanical, and electrical insulation to the backside of PV modules, but their continued functionality depends upon their ability to remain well adhered over years of harsh environmental exposure. A study of adhesive strength was conducted on several PV backsheet types exposed to indoor accelerated weathering. Two adhesion tests – the wedge test and single cantilever beam test – were used to measure adhesion energy in four backsheets: two with fluoropolymer-based outer (airside) layers – polyvinyl fluoride (PVF), polyvinylidene fluoride (PVDF) – and two with non-fluoropolymer-based outer layers–polyamide (PA) and polyethylene terephthalate (PET). The effects of changes in temperature, ultraviolet (UV) irradiance, relative humidity, and a periodic water spray were studied. The PET-, PVF- and PVDF-based backsheets all showed instances of debonding in an adhesive layer, which is commonly reported. Furthermore, for the PA-, PET-, and PVDF-based backsheets, adhesion energy dropped fairly rapidly with exposure, reaching very low levels by 4000 h. The PVF-based backsheet was relatively robust to weathering. Pull-off of an outer chalking layer in the PA- and PET-based backsheets suggested a sensitivity to UV. Adhesion in these two backsheets was also highly sensitive to changes in moisture level. Changes in UV irradiance and temperature did not show a statistically significant effect on adhesion loss for the exposure levels used. The present work is part of a two-part adhesion study on both field-weathered and indoor-exposed backsheets, and forms a basis for understanding adhesion degradation across a variety of backsheet types and degradation factors.

14 SOLAR ENERGY↗
DOE OSTI2022

Hydrogen-Bonding Bottlebrush Networks: Self-Healing Materials from Super-Soft to Stiff

The impact of polymer architecture on network dynamics and self-healing is presented using bottlebrushes containing side chains that are end-functionalized with 2-ureido-4[1H]-pyrimidinone (UPy). The synthesis of these materials is straightforward through a three-step process: (1) synthesizing rubbery poly(4-methylcaprolactone) macromonomers (p4MCL–OH) with a norbornene-based initiator, (2) functionalizing the terminal hydroxyl group with UPy–isocyanate (p4MCL–UPy), and (3) statistically copolymerizing p4MCL–OH and p4MCL–UPy via ring-opening metathesis polymerization (ROMP) to form hydrogen-bonding bottlebrushes having a fraction (p) of side chains functionalized with UPy. Attaching UPy to the free end of bottlebrush side chains dilutes the impact of friction from complementary UPy interactions on segmental dynamics, leading to a much weaker dependence of the glass-transition temperature (T g ) on p than observed in linear analogues, while the activation energy to dissociate UPy–UPy bonds (41–47 kJ/mol) remains mostly unchanged. Longer side chains result in a competition between reducing T g and inducing entanglements that influence hydrogen-bonded network dynamics. Increasing the backbone length extends the sticky Rouse region without affecting the network modulus (G x ) or UPy–UPy dissociation time (τ s ). Gx scales linearly with p and ranges from 27 kPa to 1.6 MPa, while τs remains nearly constant in contrast to linear telechelic ionomers, implying a similar self-healability across bottlebrush networks containing different amounts of UPy. Furthermore, these stretchable networks with p ≤ 0.25 undergo self-healing upon repeated rupture and melt pressing at ≤100 °C while retaining similar tensile properties. In summary, decorating bottlebrush polymers with hydrogen bonds creates opportunities to independently manipulate associative network dynamics and mechanical moduli.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A review of privacy in energy applications

As the distribution system continues to experience an increase in distributed energy resource (DER) and electric vehicle (EV) penetration, so does the need for new solutions that can help grid operators manage and leverage their capabilities. This will undoubtedly lead to new operational schemes and business opportunities that will transform the traditional consumer into a prosumer who will be more actively engaged in grid operations. Although the field is still under active development, many of the potential use cases presented in literature or industry are built upon edge computing, two-way communications, and other innovative computational constructs to attain their goals. However, at their core, many use cases assume a great level of data access to aid with the decision-making process, an assumption that may need to be revised to ensure fair and equitable operational processes are maintained. This may be particularly true as edge resources are predicted to participate in retail-side, many-to-many, or peer-to-peer markets and thus may lead to financial impacts if data access considerations are ignored. The need to revise data access mechanisms can be further justified by the introduction of new participants into the operational process, who do not have the same level of trust, nor the incentives to focus on energy delivery as their primary objective. At the same time, more consumers are becoming aware of their own data, and the potential impacts of its abuse. To help solution developers better understand these risks, this report has been developed to offer an initial introduction to the topic of privacy. This is achieved by 1) Highlighting the need for privacy-aware solutions; 2) Encouraging system designers to be inquisitive about the status quo; 3) Documenting the existing threat space; 4) Presenting and evaluating tools that may be helpful towards enabling better privacy postures; and 5) Making recommendations to encourage the adoption of better practices. From a technical perspective, the report focuses on evaluating two potential techniques by applying them to the Transactive Energy Space. Based on the obtained results, it can be established that differential privacy (DP) methods may have limited applicability when highly correlated, time-series data records need to be protected. However, DP may be a powerful tool when it is used to aggregate and analyze mid-size and large-size data sets in a more traditional statistical environment. The second tool under evaluation is threshold cryptography, which can guarantee complete secrecy (and thus privacy) but requires the establishment of key management procedures and dedicated communication channels for key coordination. Therefore, due to its increased computational overhead, the use of threshold cryptography must be weighted using a cost/benefit analysis on a per-application basis.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Extracting a mixing parameter from 2D radiographic imaging of variable-density turbulent flow

We extract a suitably averaged fluctuating density from the two-dimensional radiographic image of a flow. The X-ray attenuation is given by the Beer–Lambert law which exponentially damps the incident beam intensity by a factor proportional to the density, opacity and thickness of the target. By making reasonable assumptions for the mean density, opacity and effective thickness of the target flow, we estimate the density fluctuation contribution to the attenuation. The extracted density fluctuations averaged across the thickness of the flow in the direction of the beam may be used to form the density–specific-volume correlation $b$. In a statistical description of variable-density turbulence, $b$ quantifies the degree of mixedness. The ability to extract a measure of mixedness from experimental data would be a powerful tool that could be used in the validation of mix models. The scheme proposed is tested for DNS data computed for variable density buoyancy-driven mixing. We quantify the deficits in the extracted value of $b$ due to target thickness, Atwood number and modeled signal noise. This analysis justifies using the proposed scheme to infer the mix parameter from thin targets at moderate to low Atwood numbers. Furthermore, to illustrate how the scheme might be used in a practical problem, we demonstrate its application to a radiographic image of counter-shear flow obtained from experiments at the National Ignition Facility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗
DOE OSTI2023

Evaluation protocol for revealing magnonic contrast in TR-STXM measurements

We present a statistically motivated method to extract magnonic contrast from time-resolved scanning transmission x-ray microscopy (TR-STXM) measurements. TR-STXM is an element-specific method for resolving spin-dynamics in space and time. It offers nanometer spatial resolution and picosecond temporal resolution. The presented method makes it possible to obtain phase and amplitude profiles of spin-waves from STXM measurements. Furthermore, it allows for a rigorous transformation to reciprocal magnon k⃗-space, revealing k⃗-dependent magnon properties such as the magnon dispersion in three dimensions and for all directions of the magnetic anisotropy. We demonstrate our method using X-band ferromagnetic resonance on a micrometer-sized permalloy assembly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Statistical Uncertainty of Inhalation Dose Coefficients: Impact of Particle Deposition in ICRP 66 Human Respiratory Tract Model

Inhaled radioactive materials can pose a long-term health concern, as the material can be incorporated into the body’s metabolic pathways and remain in organs and tissues for extended durations. During the retention period, the radioactive material may localize in a source organ and irradiate adjacent target organs and tissues. Distribution of these materials changes over time, requiring biokinetic modeling to evaluate their movement through various tissues and organs. The evolving distribution depends on multiple inputs characterizing the inhaled material, such as particle size and size distribution, particle density, aspect ratio, specific radionuclide, the chemical form, and solubility. In addition, biological parameters such as breathing rate, breathing type (nasal or nasal/oral), respiratory system morphometry, tidal volume, functional residual capacity, and anatomical dead space all influence material transport. These aerosol properties and physiological characteristics of the respiratory tract jointly define a range of initial conditions that influence the time-dependent distribution of radioactive material. To evaluate both uncertainty in the initial conditions of inhalation exposure and the final output (committed effective dose) from biokinetic models, a Python-based software tool, Radiological Exposure Dose Calculator (REDCAL), was developed to propagate uncertainty within the human respiratory tract model. Focusing on deposition fraction uncertainty, the primary objective was to characterize the initial activity distribution across respiratory regions as a function of anticipated particle sizes and distributions. The impact of the deposition fraction uncertainty was propagated to committed effective dose coefficients for selected radionuclides in a companion publication. For each particle size, a lognormal distribution, characterized by its geometric mean as defined within ICRP Publication 66, serves as the basis for introducing uncertainty into the physical processes governing deposition in various lung regions. Finally, this study addresses the deposition process and examines how uncertainty in deposition mechanisms affects activity distribution in the airways, ultimately presenting the expected range and standard deviation of deposited activity as a function of particle size.

International Commission on Radiological Protectio↗
DOE OSTI2023

Spectral statistics of a minimal quantum glass model

Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the “Block Rosenzweig-Porter” (BRP) model. We calculate the spectral form factors of both models at all timescales larger than the inverse spectral width. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the steepness of the ramp of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

High Fidelity Simulations of a Methane-Oxygen Rotating Detonation Rocket Engine

The rotating detonation combustor (RDC) is an important realization of pressure gain combustion for practical applications. The RDC system is characterized by a highly unsteady flow field, with multiple reflected pressure waves following the strong detonations and the existence of partially-burnt gases entrained within the detonation annulus during the injector recovery process. While experimental efforts have provided macroscopic properties of an RDC with a given fuel-oxidizer mixture and geometry, limited optical access and reduced lifespan of flow-field diagnostic equipment constrain understanding of the mechanisms that lend to wave stability, controllability, and sustainability. To this end, high-fidelity numerical simulations of the Air Force Research Laboratory (AFRL) methane-oxygen rotating detonation rocket engine (RDRE) are performed to provide detailed insight into the detonation physics and anomalous behavior within the combustor. The results highlight the merit of high-fidelity numerical studies in analyzing the combustion processes and injector dynamics of a complex combustion system. The simulations capture the general wave behavior observed within the experimental studies. Three different operating conditions, with varying global equivalence ratio and system mass flow rate, are considered: (1) baseline configuration, (2) high equivalence ratio, and (3) high mass flow rate. The high mass flow rate case results in increased detonation wave strength whereas the high equivalence ratio results in increased deflagrative heat release. The high equivalence ratio case results in chaotic behavior with two pairs of counter-rotating detonation waves, whereas a single pair of co-rotating waves is observed in the baseline and high mass flow rate cases. Further, parasitic combustion of the reactant mixture ahead of the detonation wave diminishes its strength and reduces propagation speed to approximately 50-60\% of the Chapman-Jouguet (CJ) condition. In this work, a detailed analysis of the detonation wave behavior, injector dynamics, and the statistics of combustion parameters are presented.

Prakash, Supraj↗
DOE OSTI2024

The role of RF-induced E×B flows in the mitigation of scrape-off-layer convective transport during ion cyclotron resonance heating

Abstract While multiple experiments have reported a decrease in intermittent fluctuations in the far Scrape-Off-Layer (SOL) during ion cyclotron resonance heating (Antar et al 2010 Phys. Rev. Lett. 105 165001, Li et al 2022 Nucl. Eng. Technol. 54 207–19, Antar et al 2012 Nucl. Fusion 52 103005), the physical mechanism behind this observation has not been fully established yet. In this work, we demonstrate, for the first time, a direct correlation between the amplitude of RF-induced E×B flows and turbulence suppression in the far SOL. Using the Gas Puff Imaging (GPI) diagnostic on Alcator C-Mod, we show again that Ion Cyclotron Range of Frequencies can significantly alter the flow in the SOL and introduce a shear layer in regions magnetically connected close to the antenna (Cziegler et al 2012 Plasma Phys. Control. Fusion 54 105019). With the 4-strap field-aligned antenna operated in dipole phasing, the ratio of the power coupled by the central two straps to the power coupled by the outer two straps was varied. The resulting RF-induced radial electric field magnitude thus varied, and we show that the impact on the far SOL turbulence correlates with the modified E×B velocity. We then apply a newly-developed blob tracking algorithm (Han et al 2022 Sci. Rep. 12 18142) to higher-resolution GPI videos in order to directly observe the process of blob shearing by RF-induced E×B flows. We show that the radially sheared poloidal flows act as a transport barrier by stretching, stopping, and destroying filaments, which is consistent with the observed difference in turbulence statistics.

Diab, R. (ORCID:0000000342065868)↗
DOE OSTI2022

Incorporate day-ahead robustness and real-time incentives for electricity market design

In this paper, we propose a two-stage electricity market framework to explore the participation of distributed energy resources (DERs) in a day-ahead (DA) market and a real-time (RT) market. The objective is to determine the optimal bidding strategies of the aggregated DERs in the DA market and generate online incentive signals for DER-owners to optimize the social-welfare taking into account network operational constraints. Distributionally robust optimization is used to explicitly incorporate data-based statistical information of renewable forecasts into the supply/demand decisions in the DA market. We evaluate the conservativeness of bidding strategies distinguished by different risk aversion settings. In the RT market, a bi-level time-varying optimization problem is proposed to design the online incentive signals to tradeoff the RT imbalance penalty for distribution system operators (DSOs) and the costs of individual DER-owners. This enables tracking their optimal dispatch to provide fast balancing services, in the presence of time-varying network states while satisfying the voltage regulation requirement. Simulation results on both DA wholesale market and RT balancing market demonstrate the necessity of this two-stage design, and its robustness to uncertainties, the performance of convergence, the tracking ability and the feasibility of the resulting network operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Measurement Uncertainty in One-Of-A-Kind Event Data Analysis

A golden standard in science is to repeat an experiment a statistically significant number of times, recording data using the same set of detectors and the same data analysis methodology. In such case experimental error includes both the range of true values generated by repetitions of the experiment, and measurement uncertainty caused by the detector. They are independent. It is a huge and too frequently used simplification, to assume that one can measure multiple repetitions of an identical experiment, resulting in identical true experimental value. Repetitions, as similar is it is experimentally achievable, have unavoidable built-in differences resulting in a range of the true values rather than in a single value. When modern, very sensitive and well calibrated measurement systems are used, this range is not negligible, and sometimes dominates over the measurement uncertainty. Range of true values depends on built-in differences in physics of the experiment. Stochastic physical processes result typically in a broader range of true values than non-stochastic processes do. Measurement uncertainty depends on a measurement method (properties of the detector not of the experiment). Modern measurement methods, including digital ones, frequently make the measurement uncertainty very small. When data from one–of –a kind experiment are analyzed, only the measurement uncertainty is reported. It provides no information about the range of true experimental values, neither about reliability of a reported data point. Reliability of a data point is in general independent from its measurement uncertainty. However, in practice reliable measurement methods frequently have high measurement uncertainty, while low reliability methods are applied to limit measurement uncertainty. Comparison of reliable data with high measurement uncertainty to not so reliable data measured with low uncertainty is discussed – in different scenarios different data analysis methods are applicable. Methods for data analysis from an experiment repeated statistically significant number of times are very well developed. They do not require a detailed expertise in physics of an experiment, nor in the properties of the measurement system used, and meaning of the reported uncertainty is well understood in any scientific community. It all changes when data from one-of-a-kind experiment is analyzed. Analyst’s expertise is required both in the physics of the experiment and in all aspects of the measurement system, all possible malfunctions. Data users must remember that only measurement uncertainty is reported from any one-of-a-kind experiment. Theory with simulations may provide estimation of expected built-in differences in the experiment, and by this of expected range of true values for a given experiment; yet measurement uncertainty can never be used in place of the range of true experimental values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗