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Hidden order, revealed at scale: Supercomputing, electron ptychography uncover the inner workings of relaxor ferroelectrics

A recent study led by researchers at the Massachusetts Institute of Technology has shed new light on one of materials science’s most persistent puzzles: the elusive structural organization inside relaxor ferroelectrics. Although these materials are foundational to technologies such as precision actuators and advanced sensors, the atomic-level disorder inherent to relaxor ferroelectrics has, until now, masked the origins of their exceptional electromechanical behavior.
 
The breakthrough, highlighted in MIT News, goes beyond experimental advances; it is fundamentally computational. Central to this progress is the integration of high-resolution electron ptychography with large-scale simulation workflows powered by high-performance computing (HPC), bridging the gap between experiment and theory across various length scales.

A computational lens into atomic disorder

Relaxor ferroelectrics such as lead magnesium niobate–lead titanate (PMN-PT) exhibit what researchers describe as a “polar slush,” a complex, fluctuating arrangement of nanoscale polarization domains. Capturing this structure requires more than imaging; it demands reconstruction, simulation, and statistical interpretation of vast multidimensional datasets.
 
The MIT-led team employed multislice electron ptychography to generate 4D scanning transmission electron microscopy (4D-STEM) datasets. Each dataset consists of diffraction patterns collected across a real-space grid, yielding an immense volume of information that requires iterative reconstruction algorithms. These reconstructions rely on computational frameworks such as PtychoShelves and custom multislice solvers, tools that are computationally intensive and inherently suited to supercomputing environments.
 
Critically, the reconstruction process overcomes multiple scattering effects and retrieves depth-resolved structural information at near-atomic resolution. This allows researchers to visualize polarization variations through the thickness of the material, something unattainable with conventional microscopy techniques.

Supercomputing the physics of polarization

Beyond imaging, the study’s true computational depth emerges in its integration with molecular dynamics (MD) simulations. These simulations model supercells as large as 72 × 72 × 72 unit cells under varying strain conditions, tracking atomic displacements and polarization vectors over nanosecond timescales.
 
Such simulations are not trivial. They require:
  • Parallelized computation of interatomic forces using bond-valence models
  • Thermodynamic control via Nose–Hoover thermostats and Parrinello–Rahman barostats
  • Statistical averaging across billions of atomic interactions
The resulting datasets enable direct comparison with experimental reconstructions, effectively validating observed polar structures and revealing their dependence on strain and chemical ordering.
 
Moreover, multislice simulations of electron scattering, used to replicate experimental conditions, incorporate frozen phonon approximations with dozens of configurations to ensure convergence. 
 
These calculations, which simulate electron propagation through matter at atomic resolution, are computationally demanding and benefit significantly from HPC acceleration.

Data-driven discovery at the nanoscale

To interpret the immense data volumes, the researchers deployed advanced statistical and machine learning techniques. Principal component analysis (PCA) was applied to local polarization environments, reducing high-dimensional datasets into dominant “polar motifs” that describe recurring structural patterns.
 
Additionally, clustering algorithms were used to identify contiguous polarization domains, while pair-correlation functions quantified spatial relationships between dipoles. These analyses revealed that:
  • Polarization is strongly influenced by local chemical heterogeneity, particularly the distribution of Nb⁵⁺ and Mg²⁺ ions.
  • Short-range chemically ordered regions significantly enhance long-range polar correlations.
  • Strain drives a transition toward more ordered, ferroelectric-like behavior without eliminating intrinsic disorder.
Such findings would be inaccessible without the combination of high-resolution experimental input and large-scale computational analysis.

Resolving the limits of measurement

One of the study’s notable achievements is quantifying the resolution limits of ptychographic reconstruction. Through simulation, the team demonstrated that polar domains as small as ~1 nm can be resolved under optimal conditions, despite a depth resolution of ~3.2 nm due to inherent blurring effects.
 
This calibration, achieved through synthetic datasets and reconstruction pipelines, underscores the importance of computational modeling in interpreting experimental data. It also highlights a broader trend in materials science: measurement is no longer purely observational but deeply intertwined with simulation.

Toward predictive materials design

By bridging atomistic simulations with experimental imaging, the MIT team has effectively created a multiscale framework for understanding relaxor ferroelectrics. The implications extend beyond academic curiosity.
 
With HPC-enabled workflows, researchers can now:
  • Predict how nanoscale chemical ordering influences macroscopic properties.
  • Optimize strain conditions for enhanced electromechanical performance.
  • Design next-generation materials with tailored polarization behavior.
This convergence of supercomputing and microscopy signals a shift toward predictive materials engineering, where computation does not merely support experiments but guides them.

The supercomputing imperative

The study exemplifies how modern materials science is inseparable from high-performance computing. From reconstructing terabyte-scale microscopy datasets to simulating millions of atomic interactions, every stage of the workflow depends on computational power.
 
As datasets grow richer and models more sophisticated, the role of supercomputers will only expand, transforming hidden atomic disorder into actionable scientific insight.
 
In the case of relaxor ferroelectrics, what was once considered noise is now recognized as structure, and it is supercomputing that has made it visible.

Modeling life at the microscopic scale: A computational breakthrough in oxygen transport

Tyler O'Neal, Staff Editor LATEST
Within the human body, the delivery of oxygen occurs at the microscale, where the disciplines of physics, chemistry, and biology intersect. Elucidating the mechanisms by which oxygen is transported through the bloodstream, diffuses out of erythrocytes, and is utilized by surrounding tissues has remained a formidable challenge, primarily due to the inherent complexity of these processes.
 
Recently, a study published in the International Journal of Heat and Mass Transfer introduced a significant advancement: a fully three-dimensional computational model that simultaneously simulates oxygen transport alongside the motion and deformation of individual red blood cells (RBCs). This development constitutes an important step toward addressing one of the most complex multiphysics challenges in biomedical science.

A problem too complex to see directly

At the scale of capillaries, oxygen transport is governed by a delicate interplay of mechanisms:
  • Fluid flow through narrow vessels
  • Diffusion across multiple regions (cells, plasma, tissue)
  • Chemical reactions involving hemoglobin
  • Continuous deformation and interaction of red blood cells
Traditional models simplified this system, often ignoring individual cells or treating vessels as static tubes. But such approximations fall short of capturing how oxygen is actually delivered in living tissue.
 
The new study breaks from that tradition by embracing the full complexity.

A unified multiphysics framework

The researchers developed a diffuse interface model that unifies multiple physical processes into a single computational framework. Instead of treating boundaries, like the surface of a red blood cell, as sharp discontinuities, the method smooths them into a continuous transition region. This allows the governing equations to be solved seamlessly across the entire domain.
 
At its core, the model simultaneously solves:
  • The incompressible Navier–Stokes equations for blood flow
  • Advection–diffusion–reaction equations for oxygen transport
  • Fluid–structure interaction governing deformable red blood cells
Red blood cells are modeled as elastic membranes interacting with fluid using an immersed boundary method, enabling them to move, deform, and respond dynamically to their environment.
 
The result is a fully coupled 3D simulation where flow, chemistry, and cellular mechanics evolve together.

Capturing the behavior of living blood

One of the most striking outcomes of the study is the ability to simulate how red blood cells actively regulate oxygen delivery.
 
Rather than acting as passive carriers, the simulations suggest that RBCs:
  • Adjust oxygen release based on local tissue demand.
  • Interact with one another in ways that influence flow distribution.
  • Contribute to maintaining relatively uniform oxygenation across tissue.
This emergent behavior, arising purely from physics and chemistry, offers new insight into how the body maintains balance at the microscale.

The computational challenge beneath the surface

While the study does not explicitly reference supercomputers or high-performance computing (HPC) systems, the scale and sophistication of the model place it firmly within the realm of HPC-class workloads.
 
The simulation involves:
  • Three-dimensional, time-dependent PDEs
  • Moving and deforming interfaces
  • High-order numerical schemes (including fifth-order advection methods)
  • Coupled nonlinear physics across multiple domains
These are precisely the kinds of problems that increasingly drive demand for advanced computing infrastructure.
 
Interestingly, rather than relying solely on brute-force computational power, the researchers focused on algorithmic efficiency:
  • A mixture formulation eliminates the need for complex interface reconstruction.
  • Fixed Cartesian grids simplify geometry handling.
  • Carefully chosen numerical schemes balance accuracy and cost.
This approach reflects a broader trend in computational science: pairing smarter algorithms with scalable hardware to tackle previously intractable problems.

A glimpse of scalable biomedical simulation

The implications extend beyond this specific study. By demonstrating a practical way to simulate oxygen transport with deformable cells in 3D, the work lays a foundation for:
  • Patient-specific microcirculation modeling
  • Disease studies involving impaired oxygen delivery
  • Integration with larger-scale physiological simulations
As these models grow in size and realism, they are likely to transition naturally onto parallel and high-performance computing platforms, where their full potential can be realized.

Looking Ahead

This research highlights a subtle but important shift. The frontier of biomedical modeling is no longer defined solely by biological insight, but increasingly by computational capability.
 
Even when supercomputers are not explicitly named, they linger in the background, implicit in the complexity of the equations, the dimensionality of the models, and the ambition of the questions being asked.
 
In that sense, this study is not just about oxygen transport. It is a preview of a future where understanding life at its smallest scales depends as much on computational innovation as it does on biology itself.

Japanese scientists decode dolphin speed with supercomputing: Turbulence, vortices, and the hidden physics of propulsion

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The exceptional swimming speed and efficiency of dolphins has long intrigued researchers. Recent advances in computational science have now enabled a novel approach to this question, utilizing high-performance supercomputing rather than relying solely on empirical observation.
 
Researchers at the University of Osaka employed large-scale numerical simulations to investigate the turbulent fluid dynamics associated with dolphin locomotion. Their analysis uncovers a hierarchical organization of vortices within the flow, structures that serve as the primary drivers of propulsion, thereby advancing the scientific understanding of efficient fluid motion.

Turbulence as a computational frontier

Fluid dynamics remains one of the most computationally demanding domains in physics. Governed by the nonlinear Navier–Stokes equations, turbulent flows exhibit multiscale behavior, where energy cascades from large coherent structures down to smaller, chaotic eddies.
 
Capturing this hierarchy requires direct numerical simulation (DNS) or similarly high-resolution computational approaches, techniques that are infeasible without supercomputing infrastructure. In this study, researchers used a supercomputer to resolve the full spatiotemporal evolution of flow fields generated by oscillating dolphin tails, enabling them to:
  • Decompose turbulent flow into scale-dependent vortex structures.
  • Track energy transfer across scales (the “energy cascade”).
  • Quantify thrust contributions from different flow components.
  • Perform parameter sweeps across multiple swimming regimes.
This computational framework effectively turns the supercomputer into a “fluid microscope,” revealing details inaccessible to experimental measurement alone.

The hierarchy of vortices

The simulations demonstrate that dolphin propulsion is dominated not by the total turbulence generated, but by a hierarchical structure of vortices.
 
At the top of this hierarchy are large-scale vortex rings, generated by the oscillatory motion of the dolphin’s tail. These structures:
  • Carry the majority of the momentum transfer.
  • Push water backward efficiently.
  • Generate the bulk of forward thrust.
As these large vortices evolve, they break down into progressively smaller vortices through nonlinear interactions, a hallmark of turbulence known as the energy cascade. However, the simulations show that:
  • Small-scale vortices contribute minimally to propulsion.
  • Their role is largely dissipative, redistributing energy rather than generating thrust.
This distinction is critical. While classical turbulence theory emphasizes the complexity of small-scale structures, the Osaka team’s results indicate that biological propulsion exploits the largest coherent structures, effectively filtering useful motion from chaotic flow.
 
“Our goal is to understand which parts of the turbulent flow help dolphins swim so quickly,” noted lead researcher Yutaro Motoori, emphasizing the importance of isolating dominant flow components through computation.

Supercomputing enables flow decomposition

A key innovation in the study is the ability to computationally decompose turbulence into scale-specific contributions, a task nearly impossible in laboratory settings. By simulating the full velocity and vorticity fields, researchers could isolate:
  • Coherent vortex rings (large-scale structures).
  • Intermediate eddies contribute to energy transfer.
  • Fine-scale turbulent dissipation.
This decomposition allows for a quantitative mapping between flow structure and propulsion efficiency. The results remained robust across varying swimming speeds, suggesting a universal mechanism underlying dolphin locomotion.
 
Such insights depend critically on high-resolution simulation grids and parallel computation, where millions, or more degrees of freedom, must be solved simultaneously over time.

From biological insight to engineering design

Beyond biology, the implications of this work extend into engineering and applied physics. Understanding how dolphins harness turbulence efficiently could inform:
  • Next-generation underwater vehicles, optimized for thrust efficiency
  • Bio-inspired propulsion systems, mimicking oscillatory tail dynamics
  • Flow control strategies, reducing drag or enhancing lift in turbulent regimes
The study highlights a broader paradigm shift: rather than avoiding turbulence, advanced systems may learn to exploit its structure, guided by insights derived from supercomputing.

A curious glimpse into nature’s algorithms

Perhaps most intriguing is what this research suggests about nature itself. Dolphins, through evolution, appear to have “solved” a complex fluid dynamics problem, one that scientists are only now unraveling using some of the most powerful computational tools available.
 
By revealing that propulsion depends primarily on large-scale vortex organization rather than the full turbulent spectrum, the study offers a simpler, more elegant picture of motion in fluids.
 
It is a reminder that, in the age of supercomputing, curiosity driven science can uncover not only the mechanics of the natural world but the underlying principles that make it efficient.
 
And in this case, the answer to a deceptively simple question, why dolphins swim so fast, turns out to be written in the language of vortices, decoded by machines powerful enough to simulate the sea itself.