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Recently, Liu Jingran, a joint PhD graduate from Xi'an Jiaotong University and Leiden University in the Netherlands, along with her team members Professor Martin van Hecke and Dr. Jin Lishuai, has proposed a new design principle based on mechanical computers.

The "hysteron," which is the main subject of this study, is a unit that exhibits a "stimulus-response" hysteresis phenomenon.

In this work, the research team studied and controlled the state transition behavior of coupled hysterons based on a series-coupled bistable mechanical unit.

During this process, they reproduced some finite state machines by preparing mechanical computers.

Mechanical computers are not affected by extreme conditions such as electromagnetic radiation and temperature, so they can be used to perform computational tasks in extreme environments such as space, deep sea, and high mountains.Mechanical computers can also better ensure reliability and safety, so in special scenarios such as military, aerospace, and deep-sea exploration, they can be used to perform specific computational tasks.

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In addition, since this work is a theory-driven result, the proposed design principles are not limited to mechanical loads, but can also be extended to other physical scenarios.

Recently, the relevant paper was published in PNAS[3] with the title "Controlled pathways and sequential information processing in serially coupled mechanical hysterons". Liu Jingran is the first author and corresponding author.

Using the simplest structure possible to achieve as complex computation as possible

It is understood that for a complete computing system, it needs to have two basic modules: information processing and information storage. At the same time, it also needs to add the corresponding algorithms, input/output modules.Information storage capabilities are widely found in various materials, such as ferromagnetic materials, frustrated media, shape memory alloys, etc.

People generally use digital circuits to implement algorithm processing and information processing, such as common computers, traffic lights, vending machines, etc. in life.

However, in some extreme environments, such as extreme temperatures, circuits and power equipment are very likely to fail, leading to unreliable calculation results.

So, how should we perform calculations in this situation? Industry insiders will naturally think of the predecessor of electronic computers: mechanical computers.

The most typical examples include adders and differential machines, which can handle some common mathematical calculations. And the use of mechanical computers has reached its peak during World War II.Traditional mechanical computers were generally composed of components such as gears and bearings. They were not only structurally complex but also extremely heavy. After the rapid development of electronic computing technology in the 1970s, they gradually fell out of favor.

Nowadays, when Liu Jingran and others decided to re-examine mechanical computation, they were keen to utilize as simple a structure as possible to achieve as complex computational functions as possible.

The amorphous medium is a potential platform for realizing complex mechanical computation. Under specific loads, its internal structural units have two different stable configurations, which are the "mechanical bits" with states of "0" and "1".

There is a competitive relationship between the states of different mechanical bits, which allows the entire system to exhibit multiple stable states, thereby making it suitable for information storage.

For the different stable states of the system, they can be converted to each other by adding external loads, thereby enabling the system to have the capability to process load information.The state transition rules defined by external loads can form specific algorithms. At this time, by reasonably designing mechanical metamaterials, mechanical computation can be realized.

For frustrated media, there are interconnections and mutual influences between the units within it.

However, for previous studies in the field, they did not consider the impact of interactions on the system's state-switching behavior.

Under the condition of external loads, the state transitions of each bit are independent of each other, which greatly limits the computational power of the system.

Therefore, the team hopes to use the interactions between bits to achieve non-trivial system state transition paths, thereby enhancing the system's computational power.A Cross-Cultural Research between China and the Netherlands

It is reported that Liu Jingran's initial exposure was to the concrete "mechanical bits," which are composed of a bistable curved beam structure.

The lateral force-displacement curve of the curved beam is non-monotonic, and its external force will show a trend of "increase-decrease-increase" with displacement. At the same time, the curved beam will gradually bend in the opposite direction.

When several identical curved beams are connected in series, during the process of external load application, the external force will suddenly decrease.At the same time, the bending direction of a certain layer of curved beams will suddenly change, while the bending direction of other curved beams will remain unchanged.

During her doctoral studies at Xi'an Jiaotong University, Jingran Liu's advisor was Professor Yilun Liu. At that time, he suggested that Jingran Liu conduct in-depth research on the aforementioned behavior.

Therefore, the first topic of Jingran Liu's doctoral research was: to study the dynamic mechanical behavior of serial curved beams, and to study the impact of the number of layers on the loading and unloading behavior of serial curved beams.

Later, she found that during the process of loading and unloading, when the bending direction of one layer of curved beams suddenly changes, although the orientation of the other curved beams will not change, the deformation will decrease or increase.

As a result, she began to imagine: could different curved beams be connected in series, so that when the orientation of one curved beam changes, it drives the orientation of another curved beam to change in the opposite direction?Later on, Liu Jingran went to Leiden University in the Netherlands to participate in a joint training program. Building on her previous research experience, she continued to delve deeper into this specific field.

At that time, her collaborating professors and colleagues in the Netherlands were conducting theoretical research on the state transitions and memory behaviors of multi-stable structures.

Specifically: they referred to the bistable units that make up multi-stable structures as "hysterons" to describe the hysteresis phenomenon shown in the stimulus-response curve.

The reason for this phenomenon is due to: under the response of external stimulation, there are two different stable state paths within the unit.

As a result, during "loading-unloading," different paths will be spontaneously chosen, and a path switch will occur at a certain node, leading to the loading and unloading curves not coinciding.The two steady-state paths correspond to two different states of the hysteresis particle. For these two states, binary numbers "0" and "1" can be used to represent them.

It was also found that when the coupling effect is also taken into account, more state transition paths can be predicted theoretically.

Taking a system containing two bits as an example: without considering the coupling, when the external load increases, there is only one possible state transition path for the system, which is "00" → "01" → "11".

However, when considering the influence of series coupling, the system may exhibit another state transition path, which is "00" → "01" → "10" → "11".

Through this, not only can different response behaviors be predicted, but the increase in the system's memory capacity is also more evident.The system has added a step in the state transition process. This indicates that the range of loads it can recognize and "remember" has also increased.

At the same time, the system's state and its transition path during the loading and unloading process can be represented by a state transition graph (t-graph).

Compared with uncoupled systems, the number of state transition graphs increases significantly after the introduction of series coupling.

For example, the number of state transition graphs for a system with two bits increases from 2 to 5; for a system with three bits, it increases from 6 to 44; and for systems with more bits, the increase in the number of state transition graphs is even greater.

The research team realized that the curved beam can be used as a "mechanical bit" to concretely demonstrate the theoretical results: the two opposite orientations of the curved beam represent the two different states of the mechanical bit.At the same time, for the double-bit series system, they hope to achieve all possible switching paths, which requires the two curved beams to be connected in series.

However, a difficult problem lies in front of them: when the number of series curved beams is small, it is difficult to achieve a sudden change in the orientation of the curved beams.

The reason is: the deformation of the curved beam is continuous, and there is no obvious boundary between two different orientations, so this does not conform to the concept of "bit".

After careful deliberation, the research team found that the key to achieving a sudden change in the orientation of the curved beam is: the series system must be soft enough.

So, they found a nonlinear spring, which is composed of two rings. Subsequently, the team connected the nonlinear spring with the curved beam to increase the flexibility of the system.Subsequently, it simulated the state transition diagrams of all dual-bit series systems through finite element calculations and provided the corresponding structural parameter ranges.

Based on the simulation results, they prepared three samples, each realizing three different coupling state transition diagrams.

Next, more complex memory and computation need to be achieved. To achieve this goal, it is necessary to break the return point memory (RPM).

Return point memory is a memory effect widely present in various materials. It refers to the phenomenon where the system state returns to the previous state when the system is subjected to the previous maximum load again.

Breaking the return point memory means that the system can reach different states under cyclic loading and unloading.In the study, the research team found that: to break the regression point memory of a series system, at least three bits are needed.

By observing the state transition diagram of a three-bit system, they found that one state transition diagram described a system that broke the regression point memory twice during the loading and unloading process.

Based on this, they prepared an experimental sample - sample A, which achieved the counting function under different load histories.

Liu Jingran said: "In fact, based on the state transition diagram, not only can counting be achieved, but more complex calculations can also be realized."

In computational science, there is such an important theoretical model: the finite state machine. It is equivalent to a higher version of logical gate operations such as "AND", "OR", "NOT", etc.In logical gate operations, the system's input can directly determine the output. However, in finite state machine operations, the system's output depends not only on the input but also on the current state of the system.

Due to the addition of the "current state" variable, as well as the system's input, there are more options for the output and state, in addition to "0" and "1".

For finite state machines, they possess more powerful memory and computational capabilities compared to logical gates.

Previously, some people have implemented logical gate operations through mechanical devices. Therefore, the team hopes to achieve more complex finite state machine operations by connecting curved beam systems.

Thus, under different displacement input signals, the research team conducted a study on the state transition behavior of a three-bit series system.The results show that: Even with the same structure, different finite state machines can be achieved when different input signals are introduced.

For example: When two different quasi-static pulse displacement inputs are introduced, sample A can actually achieve 17 different finite state machines.

As for a three-bit system, it can achieve even more finite state machines. For instance, in the experiment, they have already achieved 3 finite state machines based on sample A.

Provide alternative solutions for information processing under extreme conditions.However, this study only considered the series coupling between bits, as well as the system state transition behavior under quasi-static displacement control.

Subsequently, the research group will consider more general couplings, such as parallel coupling, and situations where both series and parallel couplings coexist. At the same time, loading conditions such as force control and dynamic loads can also be taken into account.

In addition, Liu Jingran said: "Sometimes we hear some doubts about mechanical computation, such as 'mechanical computers have long been eliminated' and 'the speed of mechanical computation cannot be compared with electronic devices'."

In response, she hopes to clarify the following two points:

Firstly, compared with the mechanical computers before the advent of electronic computers, the mechanical computers developed in recent years have an essential difference.Mechanical computers of the past were primarily used for mathematical calculations. For example, even the most powerful purely mechanical computer in history—the difference engine—was only capable of performing polynomial operations and was also extremely bulky [1].

However, in recent years, research on mechanical computation has been aimed at seeking a purely mechanical method to handle non-electrical signals, thereby providing possibilities for information processing in extreme environments.

Secondly, the speed and versatility of mechanical computers indeed cannot be compared with electronic computation at present. Liu Jingran and others also do not intend to design another electronic computer.

However, in rescue scenes such as mines and gas leaks, the generation of electrical sparks may cause more serious secondary disasters.

In this situation, compared with electrically driven robots, robots with purely mechanical information processing capabilities have higher safety and reliability in disaster relief and rescue operations.Just as quantum computing only shows more advantages over traditional computers when performing specific tasks, the purpose of their research into mechanical computing is to provide an alternative method for processing information when electrical devices are not available.