102 templates · page 1 of 2
Science templates
Illustrated scientific figures for biology, chemistry, physics and mathematics, composed in the Science studio and checked as you draw: reactions balanced, dimensions analysed, constants compared with CODATA, identifiers format-checked. The source is the figure's JSON document of nodes and edges, and it opens in the Science studio rather than on the Studio canvas.
Mechanism — SN1 solvolysis of a tertiary halide
2-Bromo-2-methylpropane in aqueous ethanol: rate-determining heterolysis to the planar tert-butyl cation, fast capture by water, deprotonation to the alcohol — with the first-order rate law, racemisation and the competing E1 path all named.
Chemistry & PhysicsMechanism — SN2 with inversion of configuration
Hydroxide on (S)-2-bromobutane in a polar aprotic solvent: backside attack 180° from the C–Br bond, a single concerted transition state with no intermediate, and Walden inversion to (R)-butan-2-ol under a second-order rate law.
Chemistry & PhysicsMechanism — E1 elimination and the Zaitsev rule
2-Bromo-2-methylbutane heated in ethanol: slow ionisation to the tertiary carbocation, then loss of a β-hydrogen to a weak base, giving the more substituted Zaitsev alkene as the major product alongside SN1 substitution.
Chemistry & PhysicsCatalytic cycle — Suzuki–Miyaura cross-coupling
The four-corner palladium cycle: oxidative addition of the aryl halide, base-driven exchange to the hydroxo complex, transmetalation from the activated boronate, and reductive elimination that releases the biaryl and regenerates Pd(0).
Chemistry & PhysicsElectrochemistry — Daniell galvanic cell
Zinc and copper half-cells at 1.00 M joined by a salt bridge: oxidation at the negative anode, reduction at the positive cathode, electrons through the wire, ions through the bridge, and E°cell = +1.10 V with the Gibbs energy it implies.
Chemistry & PhysicsTitration — weak acid against strong base
25.00 cm³ of 0.100 M ethanoic acid titrated with 0.100 M NaOH: apparatus, the pH trace, and the four landmarks that matter — the acidic start, the buffer plateau, pH = pKa at half-equivalence, and an equivalence point above pH 7.
Chemistry & PhysicsDistillation — continuous ethanol/water column
A trayed fractionating column with rectifying and stripping sections around the feed tray, condenser, reflux drum and steam reboiler — plus the ethanol/water azeotrope that caps the distillate and the molecular sieve that gets past it.
Chemistry & PhysicsChromatography — reversed-phase HPLC separation
The full flow path of an RP-HPLC run: degassed aqueous/acetonitrile gradient, autosampler, guard cartridge and thermostatted C18 column into a diode-array detector — with retention factor, plate count and the Rs ≥ 1.5 acceptance rule.
Chemistry & PhysicsSpectroscopy — ¹H NMR structure elucidation
From weighing the sample into CDCl₃ to an assigned structure: lock and shim, pulse and acquire the FID, Fourier transform and phase, then read chemical shift, integration and multiplicity, confirming with ¹³C and 2-D experiments.
Chemistry & PhysicsPolymers — free-radical chain-growth of styrene
AIBN thermolysis at 65 °C through initiation, head-to-tail propagation, chain transfer and the two termination modes, ending at polystyrene with the dispersity each termination route produces and the square-root rate law.
Chemistry & PhysicsMaterials — crystal lattice types and packing
Metallic, ionic and covalent-network solids side by side: the four metal packings with their coordination numbers and packing fractions, the classic ionic structure types with their stoichiometric ratios, and diamond against graphite.
Chemistry & PhysicsPhase diagram — pressure against temperature for water
The three phase fields of water with the boundaries that separate them, the triple and critical points in numbers, the negatively sloping fusion curve that makes ice float, and the supercritical region beyond 374 °C.
Chemistry & PhysicsEquilibrium — how an acetate buffer resists pH change
An equimolar ethanoic acid / ethanoate buffer at pH 4.76: the reserves that mop up added acid and added base, Henderson–Hasselbalch, where the capacity is greatest, the working range, and what happens once the reserve runs out.
Chemistry & PhysicsGreen chemistry — two routes to ibuprofen compared
The six-step Boots synthesis with its stoichiometric aluminium chloride against the three-step BHC catalytic route: same molecule, roughly double the atom economy, recovered reagents, and far less salt waste to treat.
Chemistry & PhysicsPhysics — Free-Body Diagram Set (Four Cases)
Four worked free-body diagrams — block at rest, block on a rough incline, accelerating lift, skydiver at terminal velocity — each with forces resolved and the resulting acceleration stated.
Chemistry & PhysicsPhysics — Ray Path Through a Two-Lens System
Compound microscope ray path: the objective forms a real inverted image inside the eyepiece's focal length, and the eyepiece works as a magnifier to give a virtual final image at the near point.
Chemistry & PhysicsPhysics — Labelled DC Circuit (Series–Parallel)
A 12 V supply driving R1 in series with a parallel pair, with switch, fuse, ammeter, voltmeter, capacitor and earth labelled and every branch current and voltage worked out.
Chemistry & PhysicsPhysics — The Electromagnetic Spectrum
All seven bands from radio to gamma with wavelength, frequency and photon energy for each, the visible band expanded into its colours, and the ionising threshold marked.
Chemistry & PhysicsPhysics — Particle Decay Chain (Cosmic-Ray Air Shower)
A primary cosmic ray's hadronic cascade: pion production, π⁺ → µ⁺ decay, π⁰ → 2γ and the electromagnetic shower, with branching ratios, lifetimes and the conservation laws checked.
Chemistry & PhysicsPhysics — Two-Source Interference (Young's Double Slit)
Young's double slit with a 633 nm laser, d = 0.25 mm and L = 2.00 m: path difference, the maxima and minima conditions, and a fringe spacing of 5.06 mm worked out.
Chemistry & PhysicsPhysics — Otto Cycle (Air-Standard, Worked)
The four-process Otto cycle with every state point computed from r = 10 and γ = 1.40: pressures, temperatures, heat in and out, net work and a 60.2 % air-standard efficiency.
Chemistry & PhysicsEarth Science — The Rock Cycle
Magma through igneous, sedimentary and metamorphic rock and back, with the short-cuts across the ring, the texture evidence for cooling rate, and typical time-scales.
Geo & SpatialEarth Science — Plate Tectonic Boundaries
Divergent, subducting convergent, collisional convergent and transform boundaries side by side, each with its landforms, seismicity, volcanism and a named example.
Geo & SpatialEarth Science — The Global Water Cycle
Evaporation, advection, condensation, precipitation, runoff and groundwater with global fluxes in 10³ km³ yr⁻¹ that balance, plus store sizes and residence times.
Geo & SpatialEarth Science — Layers of the Atmosphere
The five layers and four pauses from the surface to the exosphere, each defined by the sign of its temperature gradient, with the ozone layer, Kármán line, aurorae and jet streams placed.
Geo & SpatialEarth Science — Seismic Wave Propagation
P, S, Love and Rayleigh waves leaving a focus, the layered interior they cross, and the P and S shadow zones that prove the outer core is liquid.
Geo & SpatialNitrogen cycle — fixation, nitrification, denitrification
The full soil–plant–atmosphere nitrogen cycle: biological and industrial fixation into ammonium, the two-organism nitrification chain through nitrite to nitrate, plant uptake and ammonification back from litter, and the two loss paths — nitrate leaching to groundwater and denitrification to N₂ and N₂O.
Geo & SpatialCarbon cycle — flux through a temperate forest
One year of carbon in a mature temperate stand, with every flux in g C m⁻² yr⁻¹ and the budget closing: gross primary production of 1500, half of it respired straight back by the trees, 550 respired by soil decomposers, and the 200 left over as net ecosystem production — the number that decides whether the stand is a sink.
Geo & SpatialCatchment hydrology — rainfall to river discharge
A 120 km² upland catchment routed from rain gauge to gauging station: interception and evapotranspiration, the infiltration threshold that decides between overland flow and throughflow, percolation to an unconfined aquifer, and the baseflow that keeps the river running — with P = Q + E + ΔS closing at 1400 = 950 + 450.
Geo & SpatialCirculation — the double circuit of the human heart
Both circuits drawn as one closed loop with the pressures that make them work: right side 25/4 mmHg into the lungs, left side 120/8 into the aorta, the four valves in sequence, the SA and AV nodes that time them, and a cardiac output of 70 beats × 70 mL ≈ 4.9 L min⁻¹.
Life SciencesNephron — filtration, reabsorption and secretion
One nephron from afferent arteriole to collecting duct, with the Starling pressures that drive filtration (55 − 30 − 15 = 10 mmHg), a GFR of 125 mL min⁻¹ = 180 L a day, segment-by-segment reabsorption from the proximal tubule's 65% of sodium to ADH-controlled water recovery, and the 1.5 L that finally leaves.
Life SciencesGas exchange — the alveolus and its capillary
Diffusion across the 0.5 µm blood–gas barrier drawn with the partial pressures on both sides: O₂ down a 60 mmHg gradient from alveolar 100 to venous 40, CO₂ back down only 6 mmHg because it is twenty times more soluble, equilibrium reached in 0.25 s of a 0.75 s transit, and the V̇/Q̇ ratio that decides the arterial result.
Life SciencesDigestive tract — enzymes and where absorption happens
The gut from mouth to rectum with the absorption site marked for each class of nutrient: iron and calcium in the duodenum, sugars and amino acids in the jejunum, bile salts and vitamin B₁₂ in the terminal ileum, water and sodium in the colon — plus the pH each enzyme needs and the 30 m² of villous surface it all happens across.
Life SciencesNeuron — from synaptic input to transmitter release
One signal traced end to end: summation of EPSPs at the axon hillock, the −55 mV threshold, sodium influx to +40 mV and potassium efflux back, saltatory conduction at up to 100 m s⁻¹ between nodes of Ranvier, then calcium-triggered vesicle fusion across a 20 nm cleft with a 0.5 ms synaptic delay.
Life SciencesImmune response — barrier, innate, adaptive, memory
One infection followed from breach to memory: barriers, complement and phagocytes in the first hours, antigen carried to the lymph node and shown on MHC II, helper T cells licensing B cells, clonal expansion to antibody-secreting plasma cells with IgM by day 5–7, and the memory that turns the second exposure into IgG in two days.
Life SciencesPhotosynthesis — light reactions and the Calvin cycle
Both halves on one canvas with the stoichiometry attached: water split at the oxygen-evolving complex to feed P680, electrons through plastoquinone and cytochrome b₆f pumping protons into a lumen at pH 4.5, ATP synthase at 4 H⁺ per ATP, P700 reducing NADP⁺, and the Calvin cycle spending 3 ATP and 2 NADPH per CO₂ fixed.
Life SciencesCellular respiration — glycolysis to the electron chain
Glucose to water in four stages with the ATP counted at each: 2 net plus 2 NADH from glycolysis in the cytosol, 2 NADH from the link reaction, 6 NADH, 2 FADH₂ and 2 GTP from two turns of the Krebs cycle, then oxidative phosphorylation at 2.5 ATP per NADH and 1.5 per FADH₂ for a total near 32.
Life SciencesFood web — a temperate lake through five trophic levels
A eutrophic lowland lake drawn as a web rather than a chain: phytoplankton and littoral macrophytes at 300 g C m⁻² yr⁻¹, three routes up through Daphnia, chironomids and zebra mussels, roach and perch feeding at more than one level, pike and heron on top, and the detrital loop that returns the nutrients.
Life SciencesSEIR model — compartments, rates and the R₀ threshold
The four compartments with the rate on every arrow: force of infection βI/N out of S, σ = 1/5.2 d⁻¹ through the latent period, γ = 1/7 d⁻¹ into recovery, and what follows from them — R₀ = β/γ, Rₜ = R₀S/N falling as susceptibles are used up, a peak at S/N = 1/R₀ and a herd-immunity threshold of 1 − 1/R₀.
Scientific PlotsAntibiotic resistance — how a resistant strain takes over
Selection drawn as a process rather than a warning poster: a resistant cell arising at about 10⁻⁹ per division or arriving ready-made on a plasmid, the course of treatment killing everything else, the survivor refilling the empty niche, and the MIC climbing from 0.5 to 64 mg L⁻¹ — with the stewardship and agricultural pressures that set the pace.
Life SciencesWastewater treatment — screening to tertiary polishing
A municipal works drawn as the unit-process train it is: 6 mm screens and grit removal, primary settlement taking 60% of the suspended solids, an activated-sludge lane at 3000 mg L⁻¹ MLSS with return sludge holding the age at 10 days, nitrification and anoxic denitrification, and sludge to a 35 °C digester whose biogas runs the site.
Chemistry & PhysicsBlood glucose — the negative feedback loop
Both arms of the loop around a 4.0–5.5 mmol L⁻¹ set point: a meal pushing glucose up, β cells releasing insulin and GLUT4 pulling it into muscle and fat, then α cells and glucagon driving glycogenolysis and gluconeogenesis when it falls — with the two ways the loop breaks and the HbA1c threshold that detects them.
Life SciencesCausal perturbation — loss, rescue and controls
Plan a gene-function experiment that separates association, loss-of-function and rescue. Include delivery controls and independent readouts; rescue supports specificity but does not eliminate every off-target explanation.
Life SciencesSingle-cell study — samples before cell counts
Design a single-cell analysis without treating cells from one donor as independent biological replicates. Track sample identity through quality control, annotation and donor-level comparisons.
Life SciencesOrganoid model — identity, function and limits
Validate an organoid model against predefined identity and functional criteria. Distinguish technical repeat wells from independent donor lines and make the limits of in-vitro extrapolation explicit.
Life SciencesMicrobiome workflow — contamination and compositionality
Map a sequencing study with field blanks, extraction blanks and batch randomisation. Relative abundance is compositional; absolute microbial load requires a separately justified measurement.
Life SciencesReceptor signalling — response and adaptation
A generic receptor-signalling model distinguishes ligand binding, signal amplification and termination. Feedback and receptor trafficking can alter response duration; arrows specify regulation rather than material transfer.
Life SciencesStable-isotope tracing — flux inference boundaries
Plan isotope tracing with a labelled input, time points, metabolite pools and isotopologue distributions. Enrichment alone is not flux; inference requires a network model and justified steady-state assumptions.
Life SciencesAntibody validation — orthogonal evidence
Select validation strategies for the intended assay, including genetic controls, independent antibodies and orthogonal measurements. A validation in one application does not automatically transfer to another.
Life SciencesCell migration assay — motility versus proliferation
Interpret wound closure with time-resolved imaging, viability and proliferation controls. Separate collective migration from growth and use independent cultures as the unit of replication.
Life SciencesHost–pathogen model — exposure, burden and response
A conceptual infection-study map distinguishes exposure, pathogen burden, host response and damage. Use appropriate containment and approved protocols; this template specifies measurements rather than operational pathogen-handling steps.
Life SciencesSpecies occupancy — presence versus detection
Repeated site visits help separate occupancy from imperfect detection. Keep site covariates distinct from visit-level conditions and report uncertainty rather than interpreting every non-detection as absence.
Life SciencesFood web — perturbation and indirect effects
Explore a small conceptual food web with resource limitation, predation and a perturbation. Arrow captions distinguish consumption from effects; the diagram is a hypothesis map, not a quantified stability analysis.
Life SciencesCircadian study — phase, amplitude and environment
Separate clock phase from response amplitude using time-series observations and controlled timing. Record light, feeding and sampling schedules; distinguish entrainment from a single treatment response.
Life SciencesLineage tracing — ancestry versus cell state
Track a heritable label through cell divisions while measuring phenotype separately. Clonal ancestry, current marker expression and inferred fate are different claims; label specificity and detection losses constrain interpretation.
Life SciencesImmune memory — primary and recall responses
Compare primary activation, contraction and recall in a conceptual immune-response model. Antibody titres, memory-cell frequencies and functional protection are separate readouts and should not be treated as interchangeable.
Life SciencesSpatial transcriptomics — location and mixture
Combine tissue location, expression and morphology while retaining spot-level uncertainty. Mixed-cell capture areas require explicit deconvolution assumptions; proximity alone does not establish cell-to-cell signalling.
Life SciencesEnzyme kinetics — competing inhibition models
Compare initial rates across substrate and inhibitor concentrations. Fit competing models to untransformed rates and inspect residuals; a reciprocal plot alone should not determine the inhibition mechanism.
Chemistry & PhysicsDynamic equilibrium — rates and perturbations
Distinguish equilibrium composition from equal forward and reverse rates. A concentration or temperature perturbation changes the approach to equilibrium; a catalyst changes rates without changing the equilibrium constant at fixed temperature.
Chemistry & PhysicsAnalytical method — calibration, recovery and matrix
Plan an assay validation around the intended concentration range. Calibration, matrix effects, precision and recovery answer different questions; acceptance criteria must be chosen for the measurement purpose.
Chemistry & PhysicsChromatography — retention, selectivity and efficiency
Diagnose a separation by examining retention, selectivity and peak width separately. Use a suitability mixture and replicate injections; changing one operating factor can trade resolution against analysis time.
Chemistry & PhysicsElectrochemical cell — transport and interfaces
Separate electron transport in the external circuit from ion transport through the electrolyte. Interface kinetics and mass transport both affect measured current; the reference electrode measures potential while ideally drawing negligible current.
Chemistry & PhysicsPolymer structure — synthesis to performance
Link polymer synthesis choices to molecular architecture, morphology and measured performance. Molecular mass, dispersity and crystallinity are distinct attributes; processing history can change properties without changing monomer identity.
Chemistry & PhysicsCatalyst lifetime — distinguish deactivation routes
Build a catalyst-lifetime study with activity over time and complementary characterisation. Fouling, poisoning and sintering are competing explanations, not conclusions drawn from loss of conversion alone.
Chemistry & PhysicsSpectral identification — orthogonal constraints
Combine elemental composition, functional-group evidence and connectivity constraints. A candidate structure must satisfy all observations; a database match is supporting evidence rather than proof on its own.
Chemistry & PhysicsAdsorption isotherm — mass balance and model choice
Analyse equilibrium adsorption using measured initial and equilibrium concentrations plus sorbent mass. Compare model assumptions and residuals; a good fit alone does not prove a microscopic adsorption mechanism.
Chemistry & PhysicsBattery ageing — capacity, resistance and history
Organise a battery-ageing comparison with matched operating history. Capacity loss and resistance growth are separate readouts; post-test characterisation supports mechanism hypotheses without making a single metric mechanistically definitive.
Chemistry & PhysicsProcess sustainability — boundary and functional unit
Compare two hypothetical process routes using the same functional unit and system boundary. Inventory energy, material inputs, waste and recovery separately; a high yield does not by itself establish lower environmental impact.
Chemistry & PhysicsReaction monitoring — conversion versus selectivity
Track reactant disappearance, desired-product formation and byproducts with a consistent analytical response basis. Conversion, selectivity and isolated yield describe different parts of reaction performance.
Chemistry & PhysicsMechanics — force analysis and energy cross-check
Solve a conceptual mechanics problem through both force balance and energy accounting. Define the system and reference frame first; non-conservative work and changing constraints must appear explicitly.
Scientific PlotsThermal network — storage, resistance and loss
Represent a lumped thermal system with heat capacity, conductive resistance and ambient loss. The lumped approximation must be justified before treating each body as a uniform temperature.
Scientific PlotsOptical imaging — resolution and sampling budget
Trace a microscopy image from illumination through optics and detector sampling. Optical resolution, pixel sampling, noise and motion blur impose different limits; magnification alone cannot restore missing spatial information.
Scientific PlotsVibration model — excitation, damping and modes
Distinguish imposed excitation from the measured structural response. Compare time and frequency descriptions, identify candidate modes and check whether a linear time-invariant approximation is defensible.
Scientific PlotsPipe network — continuity and pressure losses
Build a steady-flow network model with conservation at junctions and pressure losses along branches. Minor losses, elevation and pump head must use a consistent reference and unit system.
Scientific PlotsSolar collector — useful energy and losses
Account for incident, reflected, transmitted and absorbed radiation before calculating useful heat. Aperture area, irradiation period and operating temperature define the comparison basis.
Scientific PlotsMeasurement chain — calibration and uncertainty
Trace a physical measurand through sensor, conditioning, digitisation and conversion. Keep calibration bias, repeatability and environmental sensitivity separate when constructing an uncertainty budget.
Scientific PlotsWave interference — coherence and observation
Separate path difference, phase difference and coherence when predicting interference. Detector averaging and finite bandwidth can reduce fringe visibility even when the geometric path relation is unchanged.
Scientific PlotsSemiconductor device — bands, carriers and measurement
Relate a conceptual device structure to band alignment, carrier transport and terminal measurements. Contact resistance and thermal effects must be separated from intrinsic device behaviour before interpreting a curve.
Scientific PlotsRemote sensing — radiance to validated surface product
Trace a satellite observation through radiometric calibration, atmospheric correction and geolocation. Compare retrieved surface quantities with independent observations while preserving cloud and quality masks.
Scientific PlotsBayesian workflow — prior predictive to posterior checks
Organise a Bayesian analysis around a generative model, prior predictive checks, computation diagnostics and posterior predictive comparison. Sensitivity to prior and likelihood choices is part of the result.
Scientific PlotsCausal inference — estimand, graph and identification
Separate the causal question from an estimable statistical association. Specify temporal ordering and assumptions before selecting adjustment variables; conditioning on a collider can introduce bias.
Scientific PlotsConstrained optimisation — feasibility and optimality
Organise a smooth constrained optimisation problem around objective, constraints, feasible candidates and optimality checks. KKT conditions require suitable constraint qualifications and are not sufficient for arbitrary non-convex problems.
Scientific PlotsNumerical solution — consistency, stability, convergence
Plan a numerical verification study using a reference problem, mesh refinement and error norms. A visually smooth solution is not evidence of convergence; stability and implementation checks address different risks.
Scientific PlotsMarkov model — states, transitions and validation
Specify mutually exclusive states and a transition interval before estimating probabilities. Rows of the transition matrix must sum to one; homogeneity and memorylessness are assumptions to test rather than automatic properties of the data.
Scientific PlotsUncertainty propagation — inputs and dependence
Trace a derived quantity to measured inputs, sensitivity coefficients and covariance assumptions. Independent-input root-sum-squares is a special case; correlated uncertainties require covariance terms.
Scientific PlotsMissing data — mechanism and sensitivity
Describe missingness patterns before choosing an analysis. Missing-at-random assumptions cannot generally be proven from observed data; sensitivity analyses address departures from the primary assumptions.
Scientific PlotsNetwork analysis — topology versus measurement
Separate a true conceptual network from the graph observed through a sampling process. Missing nodes and edges alter centrality and communities; layout proximity is not a measured relationship.
Scientific PlotsSequential experiments — stopping and error control
Plan repeated looks at accumulating data before an experiment starts. The stopping rule, decision thresholds and multiplicity strategy belong to the design; repeatedly applying a fixed-sample threshold changes error rates.
Scientific PlotsReplication design — biological and technical units
Distinguish experimental allocation units, independent biological samples and repeated technical measurements. Aggregate or model technical repeats appropriately rather than inflating the biological sample count.
Life SciencesExperimental bias — allocation, masking and audit
Build a study workflow that keeps allocation generation, intervention delivery and outcome assessment distinct. Record unavoidable unmasking and analyse according to a predefined plan.
Life SciencesPlant stress — water status, growth and recovery
Compare plant responses during stress and after recovery. Water status, stomatal behaviour and biomass are distinct endpoints; position, developmental stage and independent plants constrain the design.
Life SciencesProteomics — peptide evidence to protein inference
Trace quantitative proteomics from independent samples through peptide identification and protein inference. Shared peptides, missing values and batch effects must remain visible in downstream comparisons.
Life SciencesMechanobiology — substrate to cellular response
Relate substrate mechanics and ligand presentation to cell adhesion, force generation and response. Changes in stiffness can be confounded by chemistry or geometry, so define matched controls.
Life SciencesBuffer design — capacity and measurement conditions
Design a buffer around target pH, working range and compatibility. Composition, dilution, temperature and added acid/base load affect performance; nominal pH alone does not describe buffer capacity.
Chemistry & PhysicsCorrosion study — exposure, electrochemistry and loss
Compare corrosion behaviour with matched surface preparation and exposure. Electrochemical indicators, mass loss and surface morphology provide complementary evidence and must use compatible time and area bases.
Chemistry & PhysicsChemical sensor — selectivity and drift
Evaluate a sensor against target concentration, interferents and time-dependent drift. A calibration in pure solution does not establish performance in a complex sample matrix.
Chemistry & PhysicsFactorial experiment — main effects and interactions
Design a two-factor experiment with every factor combination represented and replication allocated at the experimental-unit level. An interaction means the effect of one factor depends on the level of another.
Scientific PlotsPredictive modelling — split before learning
Preserve an untouched evaluation set and fit preprocessing only within training folds. Feature selection, imputation and tuning can leak outcome information if performed before splitting.
Scientific PlotsDynamical systems — equilibria and local stability
Analyse a smooth dynamical model through equilibrium solutions and a local linear approximation. Local eigenvalue behaviour does not by itself establish global stability or rule out nonlinear phenomena.
Scientific PlotsReaction–diffusion model — kinetics and transport
Separate local reaction kinetics from spatial diffusion and boundary fluxes. Spatial pattern predictions depend on parameters, initial conditions and numerical resolution; a pattern image alone does not establish mechanism.
Scientific Plots